Theorem merlem10 931

Description: Step 19 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem10	|- ((ph -> (ph -> ps)) -> (th -> (ph -> ps)))

Proof of Theorem merlem10

Step	Hyp	Ref	Expression
1		meredith 921	. 2 |- (((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph)))
2		meredith 921	. . 3 |- ((((((ph -> ps) -> ph) -> (-. ph -> -. th)) -> ph) -> ph) -> ((ph -> (ph -> ps)) -> (th -> (ph -> ps))))
3		merlem9 930	. . 3 |- (((((((ph -> ps) -> ph) -> (-. ph -> -. th)) -> ph) -> ph) -> ((ph -> (ph -> ps)) -> (th -> (ph -> ps)))) -> ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> ((ph -> (ph -> ps)) -> (th -> (ph -> ps)))))
4	2, 3	ax-mp 7	. 2 |- ((((((ph -> ph) -> (-. ph -> -. ph)) -> ph) -> ph) -> ((ph -> ph) -> (ph -> ph))) -> ((ph -> (ph -> ps)) -> (th -> (ph -> ps))))
5	1, 4	ax-mp 7	1 |- ((ph -> (ph -> ps)) -> (th -> (ph -> ps)))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  merlem11 932  suppsr2 5195

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

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