Theorem merlem2 646

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 645	. 2 |- ((((ch -> ch) -> (-. ph -> -. th)) -> ph) -> (ph -> ph))
2		meredith 644	. 2 |- (((((ch -> ch) -> (-. ph -> -. th)) -> ph) -> (ph -> ph)) -> (((ph -> ph) -> ch) -> (th -> ch)))
3	1, 2	ax-mp 6	1 |- (((ph -> ph) -> ch) -> (th -> ch))

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  merlem3 647  merlem12 656

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

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