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Theorem elabf1 11110
Description: One implication of elabf 2750. (Contributed by BJ, 21-Nov-2019.)
Hypotheses
Ref Expression
elabf1.nf  |-  F/ x ps
elabf1.1  |-  ( x  =  A  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
elabf1  |-  ( A  e.  { x  | 
ph }  ->  ps )
Distinct variable group:    x, A
Allowed substitution hints:    ph( x)    ps( x)

Proof of Theorem elabf1
StepHypRef Expression
1 nfcv 2225 . 2  |-  F/_ x A
2 elabf1.nf . 2  |-  F/ x ps
3 elabf1.1 . 2  |-  ( x  =  A  ->  ( ph  ->  ps ) )
41, 2, 3elabgf1 11108 1  |-  ( A  e.  { x  | 
ph }  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1287   F/wnf 1392    e. wcel 1436   {cab 2071
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:  elab1  11112  bj-bdfindis  11271
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