Theorem merlem8 652

Description: Step 15 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem8	|- (((ps -> ch) -> th) -> (((ch -> ta ) -> (-. th -> -. ps)) -> th))

Proof of Theorem merlem8

Step	Hyp	Ref	Expression
1		meredith 644	. 2 |- (((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph)))
2		merlem7 651	. 2 |- ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> (((ps -> ch) -> th) -> (((ch -> ta ) -> (-. th -> -. ps)) -> th)))
3	1, 2	ax-mp 6	1 |- (((ps -> ch) -> th) -> (((ch -> ta ) -> (-. th -> -. ps)) -> th))

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  merlem9 653

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

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