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Theorem wl-impchain-com-1.4 35137
 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 35133 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 (𝜂 → (𝜃 → (𝜒 → (𝜓𝜑))))
Assertion
Ref Expression
wl-impchain-com-1.4 (𝜓 → (𝜃 → (𝜒 → (𝜂𝜑))))

Proof of Theorem wl-impchain-com-1.4
StepHypRef Expression
1 wl-impchain-com-1.4.h1 . . . 4 (𝜂 → (𝜃 → (𝜒 → (𝜓𝜑))))
21wl-impchain-com-1.3 35136 . . 3 (𝜒 → (𝜃 → (𝜂 → (𝜓𝜑))))
3 wl-luk-pm2.04 35127 . . 3 ((𝜂 → (𝜓𝜑)) → (𝜓 → (𝜂𝜑)))
42, 3wl-impchain-mp-2 35132 . 2 (𝜒 → (𝜃 → (𝜓 → (𝜂𝜑))))
54wl-impchain-com-1.3 35136 1 (𝜓 → (𝜃 → (𝜒 → (𝜂𝜑))))
 Colors of variables: wff setvar class Syntax hints:   → wi 4 This theorem was proved from axioms:  ax-mp 5  ax-luk1 35101  ax-luk2 35102  ax-luk3 35103 This theorem is referenced by:  wl-impchain-com-2.4  35140
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