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Theorem riota5OLD 6331
Description: A method for computing restricted iota. (Contributed by NM, 20-Oct-2011.) (New usage 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 447 . 2  |-  ( (
ph  /\  B  e.  A )  ->  B  e.  A )
2 riota5OLD.1 . . 3  |-  ( (
ph  /\  B  e.  A  /\  x  e.  A
)  ->  ( ps  <->  x  =  B ) )
323expa 1151 . 2  |-  ( ( ( ph  /\  B  e.  A )  /\  x  e.  A )  ->  ( ps 
<->  x  =  B ) )
41, 3riota5 6330 1  |-  ( (
ph  /\  B  e.  A )  ->  ( iota_ x  e.  A ps )  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358    /\ w3a 934    = wceq 1623    e. wcel 1684   iota_crio 6297
This theorem is referenced by:  sqr0  11727  lubun  14227  odval2  14866  adjvalval  22517  unxpwdom3  27256  lubunNEW  29163  lub0N  29379  glb0N  29383  trlval2  30352  cdlemefrs32fva  30589
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-reu 2550  df-v 2790  df-sbc 2992  df-un 3157  df-if 3566  df-sn 3646  df-pr 3647  df-uni 3828  df-iota 5219  df-riota 6304
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