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Theorem riota5 5873
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 2333 . 2 (𝜑𝑥𝐵)
2 riota5.1 . 2 (𝜑𝐵𝐴)
3 riota5.2 . 2 ((𝜑𝑥𝐴) → (𝜓𝑥 = 𝐵))
41, 2, 3riota5f 5872 1 (𝜑 → (𝑥𝐴 𝜓) = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  wb 105   = wceq 1364  wcel 2160  crio 5847
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-reu 2475  df-v 2754  df-sbc 2978  df-un 3148  df-sn 3613  df-pr 3614  df-uni 3825  df-iota 5193  df-riota 5848
This theorem is referenced by:  f1ocnvfv3  5881  caucvgrelemrec  11015  sqrt0  11040  sqrtsq  11080  dfgcd3  12038
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