Theorem merlem4 1570

Description: Step 8 of Meredith's proof of Lukasiewicz axioms from his sole axiom. (Contributed by NM, 14-Dec-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem merlem4

Step	Hyp	Ref	Expression
1		meredith 1566	. 2 |- ( ( ( ( ( ph -> ph ) -> ( -. th -> -. th ) ) -> th ) -> ta ) -> ( ( ta -> ph ) -> ( th -> ph ) ) )
2		merlem3 1569	. 2 |- ( ( ( ( ( ( ph -> ph ) -> ( -. th -> -. th ) ) -> th ) -> ta ) -> ( ( ta -> ph ) -> ( th -> ph ) ) ) -> ( ta -> ( ( ta -> ph ) -> ( th -> ph ) ) ) )
3	1, 2	ax-mp 5	1 |- ( ta -> ( ( ta -> ph ) -> ( th -> ph ) ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  merlem5  1571  merlem6  1572  merlem7  1573  merlem12  1578  luk-2  1581