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Theorem sbequ12r 1652
Description: An equality theorem for substitution. (Contributed by NM, 6-Oct-2004.) (Proof shortened by Andrew Salmon, 21-Jun-2011.)
Assertion
Ref Expression
sbequ12r (x = y → ([x / y]φφ))

Proof of Theorem sbequ12r
StepHypRef Expression
1 sbequ12 1651 . . 3 (y = x → (φ ↔ [x / y]φ))
21bicomd 129 . 2 (y = x → ([x / y]φφ))
32equcoms 1591 1 (x = y → ([x / y]φφ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  [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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420
This theorem depends on definitions:  df-bi 110  df-sb 1643
This theorem is referenced by:  abbi  2148  findes  4268  opeliunxp  4337  isarep1  4926
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