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Theorem riota5OLD 6568
Description: A method for computing restricted iota. (Contributed by NM, 20-Oct-2011.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
riota5OLD.1  |-  ( (
ph  /\  B  e.  A  /\  x  e.  A
)  ->  ( ps  <->  x  =  B ) )
Assertion
Ref Expression
riota5OLD  |-  ( (
ph  /\  B  e.  A )  ->  ( iota_ x  e.  A ps )  =  B )
Distinct variable groups:    x, A    x, B    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem riota5OLD
StepHypRef Expression
1 simpr 448 . 2  |-  ( (
ph  /\  B  e.  A )  ->  B  e.  A )
2 riota5OLD.1 . . 3  |-  ( (
ph  /\  B  e.  A  /\  x  e.  A
)  ->  ( ps  <->  x  =  B ) )
323expa 1153 . 2  |-  ( ( ( ph  /\  B  e.  A )  /\  x  e.  A )  ->  ( ps 
<->  x  =  B ) )
41, 3riota5 6567 1  |-  ( (
ph  /\  B  e.  A )  ->  ( iota_ x  e.  A ps )  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359    /\ w3a 936    = wceq 1652    e. wcel 1725   iota_crio 6534
This theorem is referenced by:  sqr0  12039  odval2  15181  unxpwdom3  27224  lubunNEW  29708  lub0N  29924  glb0N  29928  trlval2  30897  cdlemefrs32fva  31134
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-reu 2704  df-v 2950  df-sbc 3154  df-un 3317  df-if 3732  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5410  df-riota 6541
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