Theorem merlem2 923

Description: Step 4 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem2	|- (((ph -> ph) -> ch) -> (th -> ch))

Proof of Theorem merlem2

Step	Hyp	Ref	Expression
1		merlem1 922	. 2 |- ((((ch -> ch) -> (-. ph -> -. th)) -> ph) -> (ph -> ph))
2		meredith 921	. 2 |- (((((ch -> ch) -> (-. ph -> -. th)) -> ph) -> (ph -> ph)) -> (((ph -> ph) -> ch) -> (th -> ch)))
3	1, 2	ax-mp 7	1 |- (((ph -> ph) -> ch) -> (th -> ch))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  merlem3 924  merlem12 933

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

Copyright terms: Public domain