 Mathbox for Wolf Lammen < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-impchain-com-1.4 Structured version   Visualization version   GIF version

Theorem wl-impchain-com-1.4 33614
 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 33610 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 33613 . . 3 (𝜒 → (𝜃 → (𝜂 → (𝜓𝜑))))
3 wl-pm2.04 33604 . . 3 ((𝜂 → (𝜓𝜑)) → (𝜓 → (𝜂𝜑)))
42, 3wl-impchain-mp-2 33609 . 2 (𝜒 → (𝜃 → (𝜓 → (𝜂𝜑))))
54wl-impchain-com-1.3 33613 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 33578  ax-luk2 33579  ax-luk3 33580 This theorem is referenced by:  wl-impchain-com-2.4  33617
 Copyright terms: Public domain W3C validator