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Theorem iotabii 5278
Description: Formula-building deduction rule for iota. (Contributed by Mario Carneiro, 2-Oct-2015.)
Hypothesis
Ref Expression
iotabii.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
iotabii  |-  ( iota
x ph )  =  ( iota x ps )

Proof of Theorem iotabii
StepHypRef Expression
1 iotabi 5265 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 iotabii.1 . 2  |-  ( ph  <->  ps )
31, 2mpg 1539 1  |-  ( iota
x ph )  =  ( iota x ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1633   iotacio 5254
This theorem is referenced by:  ovtpos  6291  riotav  6351  oppgid  14878  oppr1  15465  cbvprod  24418
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-rex 2583  df-uni 3865  df-iota 5256
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