Theorem ax3 1433

Description: Standard propositional axiom derived from Lukasiewicz axioms. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem ax3

Step	Hyp	Ref	Expression
1		luklem2 1424	. 2 |- ((-. ph -> -. ps) -> (((-. ph -> ph) -> ph) -> (ps -> ph)))
2		luklem4 1426	. 2 |- ((((-. ph -> ph) -> ph) -> (ps -> ph)) -> (ps -> ph))
3	1, 2	luklem1 1423	1 |- ((-. ph -> -. ps) -> (ps -> ph))

Syntax hints:  -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-meredith 1406

This theorem is referenced by: (None)