Theorem merlem12 938

Description: Step 28 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem12	|- (((th -> (-. -. ch -> ch)) -> ph) -> ph)

Proof of Theorem merlem12

Step	Hyp	Ref	Expression
1		merlem5 931	. . . 4 |- ((ch -> ch) -> (-. -. ch -> ch))
2		merlem2 928	. . . 4 |- (((ch -> ch) -> (-. -. ch -> ch)) -> (th -> (-. -. ch -> ch)))
3	1, 2	ax-mp 7	. . 3 |- (th -> (-. -. ch -> ch))
4		merlem4 930	. . 3 |- ((th -> (-. -. ch -> ch)) -> (((th -> (-. -. ch -> ch)) -> ph) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph)))
5	3, 4	ax-mp 7	. 2 |- (((th -> (-. -. ch -> ch)) -> ph) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph))
6		merlem11 937	. 2 |- ((((th -> (-. -. ch -> ch)) -> ph) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph)) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph))
7	5, 6	ax-mp 7	1 |- (((th -> (-. -. ch -> ch)) -> ph) -> ph)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  merlem13 939

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

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