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Theorem eqeqan12rd 2452
 Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 9-Aug-1994.)
Hypotheses
Ref Expression
eqeqan12rd.1
eqeqan12rd.2
Assertion
Ref Expression
eqeqan12rd

Proof of Theorem eqeqan12rd
StepHypRef Expression
1 eqeqan12rd.1 . . 3
2 eqeqan12rd.2 . . 3
31, 2eqeqan12d 2451 . 2
43ancoms 440 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652 This theorem is referenced by:  tfrlem5  6634  cusgrasize  21480  eigorthi  23333  axcontlem4  25899  expdiophlem2  27085  pwssplit4  27160 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-cleq 2429
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