Theorem luklem3 1425

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
luklem3	|- (ph -> (((-. ph -> ps) -> ch) -> (th -> ch)))

Proof of Theorem luklem3

Step	Hyp	Ref	Expression
1		luk-3 1422	. 2 |- (ph -> (-. ph -> -. th))
2		luklem2 1424	. 2 |- ((-. ph -> -. th) -> (((-. ph -> ps) -> ch) -> (th -> ch)))
3	1, 2	luklem1 1423	1 |- (ph -> (((-. ph -> ps) -> ch) -> (th -> ch)))

Syntax hints:  -. wn 3   -> wi 4

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

This theorem is referenced by:  luklem4  1426  luklem5  1427