Theorem merlem8 929

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 921	. 2 |- (((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph)))
2		merlem7 928	. 2 |- ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> (((ps -> ch) -> th) -> (((ch -> ta) -> (-. th -> -. ps)) -> th)))
3	1, 2	ax-mp 7	1 |- (((ps -> ch) -> th) -> (((ch -> ta) -> (-. th -> -. ps)) -> th))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  merlem9 930

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

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