Theorem wl-impchain-mp-1 33271

Description: This theorem is in fact a copy of wl-syl 33246, and repeated here to demonstrate a recursive proof scheme. The number '1' in the theorem name indicates that a chain of length 1 is modified. (Contributed by Wolf Lammen, 6-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
wl-impchain-mp-1.a	|- ( ch -> ps )
wl-impchain-mp-1.b	|- ( ps -> ph )

Assertion

Ref	Expression
wl-impchain-mp-1	|- ( ch -> ph )

Proof of Theorem wl-impchain-mp-1

Step	Hyp	Ref	Expression
1		wl-impchain-mp-1.a	. 2 |- ( ch -> ps )
2		wl-impchain-mp-1.b	. . 3 |- ( ps -> ph )
3	2	wl-imim2i 33253	. 2 |- ( ( ch -> ps ) -> ( ch -> ph ) )
4	1, 3	wl-impchain-mp-0 33270	1 |- ( ch -> ph )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-luk1 33241  ax-luk2 33242  ax-luk3 33243

This theorem is referenced by:  wl-impchain-mp-2  33272  wl-impchain-com-1.3  33276