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Theorem spv 1740
Description: Specialization, using implicit substitition. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
spv.1  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
Assertion
Ref Expression
spv  |-  ( A. x ph  ->  ps )
Distinct variable group:    ps, x
Allowed substitution hints:    ph( x, y)    ps( y)

Proof of Theorem spv
StepHypRef Expression
1 spv.1 . . 3  |-  ( x  =  y  ->  ( ph 
<->  ps ) )
21biimpd 132 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
32spimv 1692 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98   A.wal 1241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  chvarv  1812  ru  2763  nalset  3887  tfisi  4310  findcard2  6346  findcard2s  6347  bj-nalset  10015
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