Theorem merlem12 656

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 649	. . . 4 |- ((ch -> ch) -> (-. -. ch -> ch))
2		merlem2 646	. . . 4 |- (((ch -> ch) -> (-. -. ch -> ch)) -> (th -> (-. -. ch -> ch)))
3	1, 2	ax-mp 6	. . 3 |- (th -> (-. -. ch -> ch))
4		merlem4 648	. . 3 |- ((th -> (-. -. ch -> ch)) -> (((th -> (-. -. ch -> ch)) -> ph) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph)))
5	3, 4	ax-mp 6	. 2 |- (((th -> (-. -. ch -> ch)) -> ph) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph))
6		merlem11 655	. 2 |- ((((th -> (-. -. ch -> ch)) -> ph) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph)) -> (((th -> (-. -. ch -> ch)) -> ph) -> ph))
7	5, 6	ax-mp 6	1 |- (((th -> (-. -. ch -> ch)) -> ph) -> ph)

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  merlem13 657

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

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