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Theorem sbequ6 2125
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 2044 . 2  |-  F/ z  -.  A. x  x  =  y
21sbf 2117 1  |-  ( [ w  /  z ]  -.  A. x  x  =  y  <->  -.  A. x  x  =  y )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> 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-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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