Theorem wl-impchain-com-1.2 33275

Description: This theorem is in fact a copy of wl-com12 33258, and repeated here to demonstrate a simple proof scheme. The number '2' in the theorem name indicates that a chain of length 2 is modified.

See wl-impchain-com-1.x 33273 for more information how this proof is generated. (Contributed by Wolf Lammen, 7-Jul-2019.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
wl-impchain-com.1.2.a	|- ( ch -> ( ps -> ph ) )

Assertion

Ref	Expression
wl-impchain-com-1.2	|- ( ps -> ( ch -> ph ) )

Proof of Theorem wl-impchain-com-1.2

Step	Hyp	Ref	Expression
1		wl-impchain-com.1.2.a	. . . 4 |- ( ch -> ( ps -> ph ) )
2	1	wl-impchain-com-1.1 33274	. . 3 |- ( ch -> ( ps -> ph ) )
3		wl-pm2.04 33267	. . 3 |- ( ( ch -> ( ps -> ph ) ) -> ( ps -> ( ch -> ph ) ) )
4	2, 3	wl-impchain-mp-0 33270	. 2 |- ( ps -> ( ch -> ph ) )
5	4	wl-impchain-com-1.1 33274	1 |- ( ps -> ( 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-com-1.3  33276  wl-impchain-com-2.3  33279  wl-impchain-com-2.4  33280  wl-impchain-com-3.2.1  33281  wl-impchain-a1-2  33284