MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-7d Unicode version

Axiom ax-7d 2209
Description: Distinct varable version of ax-7 1535. (Contributed by Mario Carneiro, 14-Aug-2015.)
Assertion
Ref Expression
ax-7d  |-  ( A. x A. y ph  ->  A. y A. x ph )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Detailed syntax breakdown of Axiom ax-7d
StepHypRef Expression
1 wph . . . 4  wff  ph
2 vy . . . 4  set  y
31, 2wal 1532 . . 3  wff  A. y ph
4 vx . . 3  set  x
53, 4wal 1532 . 2  wff  A. x A. y ph
61, 4wal 1532 . . 3  wff  A. x ph
76, 2wal 1532 . 2  wff  A. y A. x ph
85, 7wi 6 1  wff  ( A. x A. y ph  ->  A. y A. x ph )
Colors of variables: wff set class
  Copyright terms: Public domain W3C validator