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Theorem riota5 7137
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 2983 . 2 (𝜑𝑥𝐵)
2 riota5.1 . 2 (𝜑𝐵𝐴)
3 riota5.2 . 2 ((𝜑𝑥𝐴) → (𝜓𝑥 = 𝐵))
41, 2, 3riota5f 7136 1 (𝜑 → (𝑥𝐴 𝜓) = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wa 396   = wceq 1530  wcel 2107  crio 7107
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-mo 2620  df-eu 2652  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-rex 3149  df-reu 3150  df-v 3502  df-sbc 3777  df-un 3945  df-sn 4565  df-pr 4567  df-uni 4838  df-iota 6313  df-riota 7108
This theorem is referenced by:  f1ocnvfv3  7146  sqrt0  14596  lubid  17595  lubun  17728  odval2  18615  adjvalval  29647  xdivpnfrp  30542  xrsinvgval  30597  dfgcd3  34493  poimirlem6  34784  poimirlem7  34785  lub0N  36211  glb0N  36215  trlval2  37185  cdlemefrs32fva  37422  cdleme32fva  37459  cdlemg1a  37592  unxpwdom3  39579
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