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Theorem riota5 6269
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 2630 . 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 6268 1  |-  ( ph  ->  ( iota_ x  e.  A  ps )  =  B
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369    = wceq 1379    e. wcel 1767   iota_crio 6242
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-rex 2820  df-reu 2821  df-v 3115  df-sbc 3332  df-un 3481  df-sn 4028  df-pr 4030  df-uni 4246  df-iota 5549  df-riota 6243
This theorem is referenced by:  f1ocnvfv3  6278  sqrt0  13034  lubid  15473  lubun  15606  odval2  16371  adjvalval  26532  xdivpnfrp  27297  xrsinvgval  27327  unxpwdom3  30645  lub0N  33986  glb0N  33990  trlval2  34959  cdlemefrs32fva  35196  cdleme32fva  35233  cdlemg1a  35366
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