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Theorem sbequ6 2133
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 2064 . 2  |-  F/ z  -.  A. x  x  =  y
21sbf 2125 1  |-  ( [ w  /  z ]  -.  A. x  x  =  y  <->  -.  A. x  x  =  y )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   A.wal 1397   [wsb 1747
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1621  df-nf 1625  df-sb 1748
This theorem is referenced by: (None)
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