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Theorem riota5 5633
Description: A method for computing restricted iota. (Contributed by NM, 20-Oct-2011.) (Revised by Mario Carneiro, 6-Dec-2016.)
Hypotheses
Ref Expression
riota5.1 (𝜑𝐵𝐴)
riota5.2 ((𝜑𝑥𝐴) → (𝜓𝑥 = 𝐵))
Assertion
Ref Expression
riota5 (𝜑 → (𝑥𝐴 𝜓) = 𝐵)
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem riota5
StepHypRef Expression
1 nfcvd 2229 . 2 (𝜑𝑥𝐵)
2 riota5.1 . 2 (𝜑𝐵𝐴)
3 riota5.2 . 2 ((𝜑𝑥𝐴) → (𝜓𝑥 = 𝐵))
41, 2, 3riota5f 5632 1 (𝜑 → (𝑥𝐴 𝜓) = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103   = wceq 1289  wcel 1438  crio 5607
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-eu 1951  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-ral 2364  df-rex 2365  df-reu 2366  df-v 2621  df-sbc 2841  df-un 3003  df-sn 3452  df-pr 3453  df-uni 3654  df-iota 4980  df-riota 5608
This theorem is referenced by:  f1ocnvfv3  5641  caucvgrelemrec  10412  sqrt0  10437  sqrtsq  10477  dfgcd3  11277
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