Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  axc711to11 Structured version   Visualization version   GIF version

Theorem axc711to11 34521
Description: Rederivation of ax-11 2074 from axc711 34518. Note that ax-c7 34489 and ax-11 2074 are not used by the rederivation. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc711to11 (∀𝑥𝑦𝜑 → ∀𝑦𝑥𝜑)

Proof of Theorem axc711to11
StepHypRef Expression
1 axc711toc7 34520 . . 3 (¬ ∀𝑦 ¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑 → ¬ ∀𝑥𝑦𝜑)
21con4i 113 . 2 (∀𝑥𝑦𝜑 → ∀𝑦 ¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑)
3 axc711 34518 . . 3 (¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑 → ∀𝑥𝜑)
43alimi 1779 . 2 (∀𝑦 ¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑 → ∀𝑦𝑥𝜑)
52, 4syl 17 1 (∀𝑥𝑦𝜑 → ∀𝑦𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-11 2074  ax-c5 34487  ax-c4 34488  ax-c7 34489
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator