Theorem ax3 671

Description: Standard propositional axiom derived from Lukasiewicz axioms.

Assertion

Ref	Expression
ax3	|- ((-. ph -> -. ps) -> (ps -> ph))

Proof of Theorem ax3

Step	Hyp	Ref	Expression
1		luklem2 662	. 2 |- ((-. ph -> -. ps) -> (((-. ph -> ph) -> ph) -> (ps -> ph)))
2		luklem4 664	. 2 |- ((((-. ph -> ph) -> ph) -> (ps -> ph)) -> (ps -> ph))
3	1, 2	luklem1 661	1 |- ((-. ph -> -. ps) -> (ps -> ph))

Syntax hints:  -. wn 1   -> wi 2

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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