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Theorem sbequ12a 1634
Description: An equality theorem for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbequ12a (x = y → ([y / x]φ ↔ [x / y]φ))

Proof of Theorem sbequ12a
StepHypRef Expression
1 sbequ12 1632 . 2 (x = y → (φ ↔ [y / x]φ))
2 sbequ12 1632 . . 3 (y = x → (φ ↔ [x / y]φ))
32equcoms 1572 . 2 (x = y → (φ ↔ [x / y]φ))
41, 3bitr3d 179 1 (x = y → ([y / x]φ ↔ [x / y]φ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  [wsb 1623
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 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-4 1377  ax-17 1396  ax-i9 1400
This theorem depends on definitions:  df-bi 110  df-sb 1624
This theorem is referenced by: (None)
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