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Theorem iotabii 5015
Description: Formula-building deduction 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 5002 . 2 (∀𝑥(𝜑𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
2 iotabii.1 . 2 (𝜑𝜓)
31, 2mpg 1386 1 (℩𝑥𝜑) = (℩𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wb 104   = wceq 1290  cio 4991
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-uni 3660  df-iota 4993
This theorem is referenced by:  riotav  5627  cbvsum  10803
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