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Theorem wl-impchain-com-1.2 33591
Description: This theorem is in fact a copy of wl-com12 33574, 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 33589 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 (𝜒 → (𝜓𝜑))
Assertion
Ref Expression
wl-impchain-com-1.2 (𝜓 → (𝜒𝜑))

Proof of Theorem wl-impchain-com-1.2
StepHypRef Expression
1 wl-impchain-com.1.2.a . . . 4 (𝜒 → (𝜓𝜑))
21wl-impchain-com-1.1 33590 . . 3 (𝜒 → (𝜓𝜑))
3 wl-pm2.04 33583 . . 3 ((𝜒 → (𝜓𝜑)) → (𝜓 → (𝜒𝜑)))
42, 3wl-impchain-mp-0 33586 . 2 (𝜓 → (𝜒𝜑))
54wl-impchain-com-1.1 33590 1 (𝜓 → (𝜒𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-luk1 33557  ax-luk2 33558  ax-luk3 33559
This theorem is referenced by:  wl-impchain-com-1.3  33592  wl-impchain-com-2.3  33595  wl-impchain-com-2.4  33596  wl-impchain-com-3.2.1  33597  wl-impchain-a1-2  33600
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