Theorem wl-syls1 33291

Description: Replacing a nested consequent. A sort of syllogism in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
wl-syls1.1	|- ( ps -> ch )
wl-syls1.2	|- ( ( ph -> ch ) -> th )

Assertion

Ref	Expression
wl-syls1	|- ( ( ph -> ps ) -> th )

Proof of Theorem wl-syls1

Step	Hyp	Ref	Expression
1		wl-syls1.1	. . 3 |- ( ps -> ch )
2	1	a1i 11	. 2 |- ( ph -> ( ps -> ch ) )
3		wl-syls1.2	. 2 |- ( ( ph -> ch ) -> th )
4	2, 3	wl-mps 33290	1 |- ( ( ph -> ps ) -> th )

Syntax hints:   -> wi 4

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

This theorem is referenced by: (None)