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Theorem vtocleg 2757
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Jan-2004.)
Hypothesis
Ref Expression
vtocleg.1  |-  ( x  =  A  ->  ph )
Assertion
Ref Expression
vtocleg  |-  ( A  e.  V  ->  ph )
Distinct variable groups:    x, A    ph, x
Allowed substitution hint:    V( x)

Proof of Theorem vtocleg
StepHypRef Expression
1 elisset 2700 . 2  |-  ( A  e.  V  ->  E. x  x  =  A )
2 vtocleg.1 . . 3  |-  ( x  =  A  ->  ph )
32exlimiv 1577 . 2  |-  ( E. x  x  =  A  ->  ph )
41, 3syl 14 1  |-  ( A  e.  V  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331   E.wex 1468    e. wcel 1480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688
This theorem is referenced by:  vtocle  2760  spsbc  2920  prexg  4133  funimaexglem  5206  eloprabga  5858  cc3  7088  bj-prexg  13168
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