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Theorem riota5OLD 6505
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 6504 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 1649    e. wcel 1717   iota_crio 6471
This theorem is referenced by:  sqr0  11967  odval2  15109  unxpwdom3  26918  lubunNEW  29139  lub0N  29355  glb0N  29359  trlval2  30328  cdlemefrs32fva  30565
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ral 2647  df-rex 2648  df-reu 2649  df-v 2894  df-sbc 3098  df-un 3261  df-if 3676  df-sn 3756  df-pr 3757  df-uni 3951  df-iota 5351  df-riota 6478
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