Mathbox for Wolf Lammen < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-impchain-com-1.2 Structured version   Visualization version   GIF version

Theorem wl-impchain-com-1.2 35135
 Description: This theorem is in fact a copy of wl-luk-com12 35118, 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 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.1.2.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 35134 . . 3 (𝜒 → (𝜓𝜑))
3 wl-luk-pm2.04 35127 . . 3 ((𝜒 → (𝜓𝜑)) → (𝜓 → (𝜒𝜑)))
42, 3wl-impchain-mp-0 35130 . 2 (𝜓 → (𝜒𝜑))
54wl-impchain-com-1.1 35134 1 (𝜓 → (𝜒𝜑))
 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-1.3  35136  wl-impchain-com-2.3  35139  wl-impchain-com-2.4  35140  wl-impchain-com-3.2.1  35141  wl-impchain-a1-2  35144
 Copyright terms: Public domain W3C validator