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 33003
Description: Rederivation of ax-11 2020 from axc711 33000. Note that ax-c7 32971 and ax-11 2020 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 33002 . . 3 (¬ ∀𝑦 ¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑 → ¬ ∀𝑥𝑦𝜑)
21con4i 111 . 2 (∀𝑥𝑦𝜑 → ∀𝑦 ¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑)
3 axc711 33000 . . 3 (¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑 → ∀𝑥𝜑)
43alimi 1729 . 2 (∀𝑦 ¬ ∀𝑦 ¬ ∀𝑥𝑦𝜑 → ∀𝑦𝑥𝜑)
52, 4syl 17 1 (∀𝑥𝑦𝜑 → ∀𝑦𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-11 2020  ax-c5 32969  ax-c4 32970  ax-c7 32971
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator