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Theorem sbequ6 1972
Description: Substitution does not change a distinctor. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequ6  |-  ( [ w  /  z ]  -.  A. x  x  =  y  <->  -.  A. x  x  =  y )

Proof of Theorem sbequ6
StepHypRef Expression
1 nfnae 1896 . 2  |-  F/ z  -.  A. x  x  =  y
21sbf 1966 1  |-  ( [ w  /  z ]  -.  A. x  x  =  y  <->  -.  A. x  x  =  y )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> 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-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
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