 Mathbox for Wolf Lammen < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-impchain-com-1.3 Structured version   Visualization version   GIF version

Theorem wl-impchain-com-1.3 33588
 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 33585 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 (𝜃 → (𝜒 → (𝜓𝜑)))
Assertion
Ref Expression
wl-impchain-com-1.3 (𝜓 → (𝜒 → (𝜃𝜑)))

Proof of Theorem wl-impchain-com-1.3
StepHypRef Expression
1 wl-impchain-com-1.3.h1 . . . 4 (𝜃 → (𝜒 → (𝜓𝜑)))
21wl-impchain-com-1.2 33587 . . 3 (𝜒 → (𝜃 → (𝜓𝜑)))
3 wl-pm2.04 33579 . . 3 ((𝜃 → (𝜓𝜑)) → (𝜓 → (𝜃𝜑)))
42, 3wl-impchain-mp-1 33583 . 2 (𝜒 → (𝜓 → (𝜃𝜑)))
54wl-impchain-com-1.2 33587 1 (𝜓 → (𝜒 → (𝜃𝜑)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4 This theorem was proved from axioms:  ax-mp 5  ax-luk1 33553  ax-luk2 33554  ax-luk3 33555 This theorem is referenced by:  wl-impchain-com-1.4  33589  wl-impchain-com-2.3  33591
 Copyright terms: Public domain W3C validator