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Theorem symdifeq2 3809
Description: Equality theorem for symmetric difference. (Contributed by Scott Fenton, 24-Apr-2012.)
Assertion
Ref Expression
symdifeq2 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))

Proof of Theorem symdifeq2
StepHypRef Expression
1 symdifeq1 3808 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
2 symdifcom 3807 . 2 (𝐶𝐴) = (𝐴𝐶)
3 symdifcom 3807 . 2 (𝐶𝐵) = (𝐵𝐶)
41, 2, 33eqtr4g 2669 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1475  csymdif 3805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-symdif 3806
This theorem is referenced by: (None)
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