Theorem wl-impchain-com-1.3 33276

Description: This theorem is in fact a copy of com13 88, and repeated here to demonstrate a simple proof scheme. The number '3' in the theorem name indicates that a chain of length 3 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-1.3.h1	|- ( th -> ( ch -> ( ps -> ph ) ) )

Assertion

Ref	Expression
wl-impchain-com-1.3	|- ( ps -> ( ch -> ( th -> ph ) ) )

Proof of Theorem wl-impchain-com-1.3

Step	Hyp	Ref	Expression
1		wl-impchain-com-1.3.h1	. . . 4 |- ( th -> ( ch -> ( ps -> ph ) ) )
2	1	wl-impchain-com-1.2 33275	. . 3 |- ( ch -> ( th -> ( ps -> ph ) ) )
3		wl-pm2.04 33267	. . 3 |- ( ( th -> ( ps -> ph ) ) -> ( ps -> ( th -> ph ) ) )
4	2, 3	wl-impchain-mp-1 33271	. 2 |- ( ch -> ( ps -> ( th -> ph ) ) )
5	4	wl-impchain-com-1.2 33275	1 |- ( ps -> ( ch -> ( th -> 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-1.4  33277  wl-impchain-com-2.3  33279