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Theorem elab1 14888
Description: One implication of elab 2893. (Contributed by BJ, 21-Nov-2019.)
Hypothesis
Ref Expression
elab1.1  |-  ( x  =  A  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
elab1  |-  ( A  e.  { x  | 
ph }  ->  ps )
Distinct variable groups:    ps, x    x, A
Allowed substitution hint:    ph( x)

Proof of Theorem elab1
StepHypRef Expression
1 nfv 1538 . 2  |-  F/ x ps
2 elab1.1 . 2  |-  ( x  =  A  ->  ( ph  ->  ps ) )
31, 2elabf1 14886 1  |-  ( A  e.  { x  | 
ph }  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1363    e. wcel 2158   {cab 2173
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751
This theorem is referenced by: (None)
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