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Theorem riota5 6577
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 2575 . 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 6576 1  |-  ( ph  ->  ( iota_ x  e.  A ps )  =  B
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    /\ wa 360    = wceq 1653    e. wcel 1726   iota_crio 6544
This theorem is referenced by:  riota5OLD  6578  f1ocnvfv3  6587  lubid  14441  lubun  14552  adjvalval  23442  xdivpnfrp  24181  xrsinvgval  24201  cdleme32fva  31296  cdlemg1a  31429
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  df-v 2960  df-sbc 3164  df-un 3327  df-if 3742  df-sn 3822  df-pr 3823  df-uni 4018  df-iota 5420  df-riota 6551
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