Theorem merlem11 655

Description: Step 20 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem11	|- ((ph -> (ph -> ps)) -> (ph -> ps))

Proof of Theorem merlem11

Step	Hyp	Ref	Expression
1		meredith 644	. 2 |- (((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph)))
2		merlem10 654	. . 3 |- ((ph -> (ph -> ps)) -> ((ph -> (ph -> ps)) -> (ph -> ps)))
3		merlem10 654	. . 3 |- (((ph -> (ph -> ps)) -> ((ph -> (ph -> ps)) -> (ph -> ps))) -> ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> ((ph -> (ph -> ps)) -> (ph -> ps))))
4	2, 3	ax-mp 6	. 2 |- ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> ((ph -> (ph -> ps)) -> (ph -> ps)))
5	1, 4	ax-mp 6	1 |- ((ph -> (ph -> ps)) -> (ph -> ps))

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  merlem12 656  merlem13 657  luk-2 659  luk-3 660

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

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