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Theorem sbequ12a 1921
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 1919 . 2 (x = y → (φ ↔ [y / x]φ))
2 sbequ12 1919 . . 3 (y = x → (φ ↔ [x / y]φ))
32equcoms 1681 . 2 (x = y → (φ ↔ [x / y]φ))
41, 3bitr3d 246 1 (x = y → ([y / x]φ ↔ [x / y]φ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-sb 1649
This theorem is referenced by:  sbco3  2088
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