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Theorem iotabii 4889
 Description: Formula-building deduction rule for iota. (Contributed by Mario Carneiro, 2-Oct-2015.)
Hypothesis
Ref Expression
iotabii.1 (𝜑𝜓)
Assertion
Ref Expression
iotabii (℩𝑥𝜑) = (℩𝑥𝜓)

Proof of Theorem iotabii
StepHypRef Expression
1 iotabi 4876 . 2 (∀𝑥(𝜑𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
2 iotabii.1 . 2 (𝜑𝜓)
31, 2mpg 1340 1 (℩𝑥𝜑) = (℩𝑥𝜓)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1243  ℩cio 4865 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-uni 3581  df-iota 4867 This theorem is referenced by:  riotav  5473
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