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Axiom ax-11d 2239
Description: Distinct varable version of ax-11 1715. (Contributed by Mario Carneiro, 14-Aug-2015.)
Assertion
Ref Expression
ax-11d  |-  ( x  =  y  ->  ( A. y ph  ->  A. x
( x  =  y  ->  ph ) ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Detailed syntax breakdown of Axiom ax-11d
StepHypRef Expression
1 vx . . 3  set  x
2 vy . . 3  set  y
31, 2weq 1624 . 2  wff  x  =  y
4 wph . . . 4  wff  ph
54, 2wal 1527 . . 3  wff  A. y ph
63, 4wi 4 . . . 4  wff  ( x  =  y  ->  ph )
76, 1wal 1527 . . 3  wff  A. x
( x  =  y  ->  ph )
85, 7wi 4 . 2  wff  ( A. y ph  ->  A. x
( x  =  y  ->  ph ) )
93, 8wi 4 1  wff  ( x  =  y  ->  ( A. y ph  ->  A. x
( x  =  y  ->  ph ) ) )
Colors of variables: wff set class
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