Graphing Principia Mathematica Ep8; Specific Theorems 1: *3.22; "Dangling Implication Substitution"

This is the first episode among the Graphing Principia episodes in which I take a look at an already-mapped, specific theorem to demonstrate a concept, or idea, or what-have-you, that I felt needed fleshing out for anyone curious. This first 'Specific Theorems' segment is about what I call the 'dangling implication substitution' that is seen somewhat rarely (at least in the first two chapters) and how it works. It's a nightmare to wrap one's head around, even if you understand it, so I figured it made the perfect first specimen for a video in this series-within-a-series. The below is as usual the regular description text for these, I want to add though that the next one will be much shorter and focused on a single theorem that I really want to just have a single video dedicated to because I find its justification particularly elegant and want to go through it step-by-step when I figure out how to set up a sort of 'meta-chart studio' for going through it. Hello! I'm not sure how many of these I'm going to do but, while I certainly won't record all of the process and upload it, I figured it'd be a cool thing to do to record and upload at least some of it. If for no other reason than to help me catch errors. Anyway if you like this video please give it a thumbs up or if you are interested in my other stuff check out the TPM companion playlist on my channel. Thank you for watching!