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Theorem iotabii 5440
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 5427 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( iota x ph )  =  ( iota x ps ) )
2 iotabii.1 . 2  |-  ( ph  <->  ps )
31, 2mpg 1557 1  |-  ( iota
x ph )  =  ( iota x ps )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    = wceq 1652   iotacio 5416
This theorem is referenced by:  ovtpos  6494  riotav  6554  oppgid  15152  oppr1  15739  cbvprod  25241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-uni 4016  df-iota 5418
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