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Theorem elab2a 10745
Description: One implication of elab 2739. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
elab2a.s  |-  A  e. 
_V
elab2a.1  |-  ( x  =  A  ->  ( ps  ->  ph ) )
Assertion
Ref Expression
elab2a  |-  ( ps 
->  A  e.  { x  |  ph } )
Distinct variable groups:    ps, x    x, A
Allowed substitution hint:    ph( x)

Proof of Theorem elab2a
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ps
2 elab2a.s . 2  |-  A  e. 
_V
3 elab2a.1 . 2  |-  ( x  =  A  ->  ( ps  ->  ph ) )
41, 2, 3elabf2 10743 1  |-  ( ps 
->  A  e.  { x  |  ph } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    e. wcel 1434   {cab 2068   _Vcvv 2602
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604
This theorem is referenced by: (None)
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