Theorem luklem5 1427

Description: Used to rederive standard propositional axioms from Lukasiewicz'. (Contributed by NM, 22-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem luklem5

Step	Hyp	Ref	Expression
1		luklem3 1425	. 2 |- (ph -> (((-. ph -> ph) -> ph) -> (ps -> ph)))
2		luklem4 1426	. 2 |- ((((-. ph -> ph) -> ph) -> (ps -> ph)) -> (ps -> ph))
3	1, 2	luklem1 1423	1 |- (ph -> (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:  luklem6  1428  luklem7  1429  ax1  1431