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Theorem sbh 2230
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 14-May-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 1682 . 2  |-  F/ x ph
32sbf 2229 1  |-  ( [ y  /  x ] ph 
<-> 
ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 189   A.wal 1450   [wsb 1805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806
This theorem is referenced by: (None)
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