Theorem luklem5 665

Description: Lemma for rederiving standard propositional axioms from Lukasiewicz'.

Assertion

Ref	Expression
luklem5	|- (ph -> (ps -> ph))

Proof of Theorem luklem5

Step	Hyp	Ref	Expression
1		luklem3 663	. 2 |- (ph -> (((-. ph -> ph) -> ph) -> (ps -> ph)))
2		luklem4 664	. 2 |- ((((-. ph -> ph) -> ph) -> (ps -> ph)) -> (ps -> ph))
3	1, 2	luklem1 661	1 |- (ph -> (ps -> ph))

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  luklem6 666  luklem7 667  ax1 669

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

metamath.org