MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  2ax5 Structured version   Visualization version   GIF version

Theorem 2ax5 1938
Description: Quantification of two variables over a formula in which they do not occur. (Contributed by Alan Sare, 12-Apr-2011.)
Ref Expression
2ax5 (𝜑 → ∀𝑥𝑦𝜑)
Distinct variable groups:   𝜑,𝑥   𝜑,𝑦

Proof of Theorem 2ax5
StepHypRef Expression
1 id 22 . 2 (𝜑𝜑)
21alrimivv 1929 1 (𝜑 → ∀𝑥𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1797  ax-4 1811  ax-5 1911
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator