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Theorem sbh 2106
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 1560 . 2  |-  F/ x ph
32sbf 2105 1  |-  ( [ y  /  x ] ph 
<-> 
ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549   [wsb 1658
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659
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