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Theorem riota5 5518
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  |-  ( ph  ->  B  e.  A )
riota5.2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  x  =  B ) )
Assertion
Ref Expression
riota5  |-  ( ph  ->  ( iota_ x  e.  A  ps )  =  B
)
Distinct variable groups:    x, A    x, B    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem riota5
StepHypRef Expression
1 nfcvd 2221 . 2  |-  ( ph  -> 
F/_ x B )
2 riota5.1 . 2  |-  ( ph  ->  B  e.  A )
3 riota5.2 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  x  =  B ) )
41, 2, 3riota5f 5517 1  |-  ( ph  ->  ( iota_ x  e.  A  ps )  =  B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103    = wceq 1285    e. wcel 1434   iota_crio 5492
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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-reu 2356  df-v 2604  df-sbc 2817  df-un 2978  df-sn 3406  df-pr 3407  df-uni 3604  df-iota 4891  df-riota 5493
This theorem is referenced by:  f1ocnvfv3  5526  caucvgrelemrec  9992  sqrt0  10017  sqrtsq  10057  dfgcd3  10532
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