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Theorem sbh 1967
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
sbh.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
sbh  |-  ( [ y  /  x ] ph 
<-> 
ph )

Proof of Theorem sbh
StepHypRef Expression
1 sbh.1 . . 3  |-  ( ph  ->  A. x ph )
21nfi 1538 . 2  |-  F/ x ph
32sbf 1966 1  |-  ( [ y  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527   [wsb 1629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-sb 1630
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