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Theorem sbequ6 1663
Description: Substitution does not change a distinctor. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 14-May-2005.)
Assertion
Ref Expression
sbequ6 ([w / z] ¬ x x = y ↔ ¬ x x = y)

Proof of Theorem sbequ6
StepHypRef Expression
1 nfnae 1607 . 2 z ¬ x x = y
21sbf 1657 1 ([w / z] ¬ x x = y ↔ ¬ x x = y)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98  wal 1240  [wsb 1642
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643
This theorem is referenced by: (None)
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