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Theorem symdifeq2 3982
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 3981 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
2 symdifcom 3980 . 2 (𝐶𝐴) = (𝐴𝐶)
3 symdifcom 3980 . 2 (𝐶𝐵) = (𝐵𝐶)
41, 2, 33eqtr4g 2811 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1624  csymdif 3978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046  ax-7 2082  ax-9 2140  ax-10 2160  ax-11 2175  ax-12 2188  ax-13 2383  ax-ext 2732
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1627  df-ex 1846  df-nf 1851  df-sb 2039  df-clab 2739  df-cleq 2745  df-clel 2748  df-nfc 2883  df-ral 3047  df-rab 3051  df-v 3334  df-dif 3710  df-un 3712  df-symdif 3979
This theorem is referenced by: (None)
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