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Theorem elab2a 11113
Description: One implication of elab 2751. (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 1464 . 2  |-  F/ x ps
2 elab2a.s . 2  |-  A  e. 
_V
3 elab2a.1 . 2  |-  ( x  =  A  ->  ( ps  ->  ph ) )
41, 2, 3elabf2 11111 1  |-  ( ps 
->  A  e.  { x  |  ph } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287    e. wcel 1436   {cab 2071   _Vcvv 2615
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617
This theorem is referenced by: (None)
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