Theorem wl-impchain-com-1.4 33277

Description: This theorem is in fact a copy of com14 96, and repeated here to demonstrate a simple proof scheme. The number '4' in the theorem name indicates that a chain of length 4 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-1.4.h1	|- ( et -> ( th -> ( ch -> ( ps -> ph ) ) ) )

Assertion

Ref	Expression
wl-impchain-com-1.4	|- ( ps -> ( th -> ( ch -> ( et -> ph ) ) ) )

Proof of Theorem wl-impchain-com-1.4

Step	Hyp	Ref	Expression
1		wl-impchain-com-1.4.h1	. . . 4 |- ( et -> ( th -> ( ch -> ( ps -> ph ) ) ) )
2	1	wl-impchain-com-1.3 33276	. . 3 |- ( ch -> ( th -> ( et -> ( ps -> ph ) ) ) )
3		wl-pm2.04 33267	. . 3 |- ( ( et -> ( ps -> ph ) ) -> ( ps -> ( et -> ph ) ) )
4	2, 3	wl-impchain-mp-2 33272	. 2 |- ( ch -> ( th -> ( ps -> ( et -> ph ) ) ) )
5	4	wl-impchain-com-1.3 33276	1 |- ( ps -> ( th -> ( ch -> ( et -> 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-2.4  33280