Users' Mathboxes Mathbox for Norm Megill < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  a7swAUX7 Unicode version

Theorem a7swAUX7 29422
Description: Weak version of a7s 1721 not requiring ax-7 1720. (Contributed by NM, 28-Oct-2017.)
Hypothesis
Ref Expression
a7sw.1  |-  ( A. x A. y ph  ->  ps )
Assertion
Ref Expression
a7swAUX7  |-  ( A. y A. x ph  ->  ps )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)    ps( x, y)

Proof of Theorem a7swAUX7
StepHypRef Expression
1 ax7vAUX7 29420 . 2  |-  ( A. y A. x ph  ->  A. x A. y ph )
2 a7sw.1 . 2  |-  ( A. x A. y ph  ->  ps )
31, 2syl 15 1  |-  ( A. y A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530
This theorem is referenced by:  cbv3hvNEW7  29423  cbv1hwAUX7  29488  cbv2hwAUX7  29490
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8  ax-7v 29419
  Copyright terms: Public domain W3C validator