Proof of "Axioms" of Propositional Logic: Synopsis

[talanum1]

Note that there is a space next to an Attractor: "...-->--( ..." and not next to a bracket: "...-->--((...".

[talanum1]

Actually we must restrict A:AM so that we can't prove "(A)--(x)--(B)" from "(A)--(+)--(B)" for example. Thus we need axioms:

A:AM2: )--(x)-- ((A) []--(+)--(B)) <> )--(x)--(A) []--(+)--(B)

where we see the attractor not going to "(B)" too. Similarly:

A:AM3: )--(x)-- ((A) []-->--(B)) <> )--(x)--(A) []-->--(B)

and:

A:AM4: )--(+)-- ((A) []-->--(B)) <> )--(+)--(A) []-->--(B)

and:

A:AM5: )---- ((A) []--(+)--(B)) <> )----(A) []--(+)--(B)

where "----" means: "is relevant to", and

A:AM6: )---- ((A) []-->--(B)) <> )----(A) []-->--(B).