Theorem merlem4 927

Description: Step 8 of Meredith's proof of Lukasiewicz axioms from his sole axiom.

Assertion

Ref	Expression
merlem4	|- (ta -> ((ta -> ph) -> (th -> ph)))

Proof of Theorem merlem4

Step	Hyp	Ref	Expression
1		meredith 923	. 2 |- (((((ph -> ph) -> (-. th -> -. th)) -> th) -> ta) -> ((ta -> ph) -> (th -> ph)))
2		merlem3 926	. 2 |- ((((((ph -> ph) -> (-. th -> -. th)) -> th) -> ta) -> ((ta -> ph) -> (th -> ph))) -> (ta -> ((ta -> ph) -> (th -> ph))))
3	1, 2	ax-mp 7	1 |- (ta -> ((ta -> ph) -> (th -> ph)))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  merlem5 928  merlem6 929  merlem7 930  merlem12 935  luk-2 938

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

Copyright terms: Public domain