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Theorem symdifeq2 4248
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 4247 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
2 symdifcom 4246 . 2 (𝐶𝐴) = (𝐴𝐶)
3 symdifcom 4246 . 2 (𝐶𝐵) = (𝐵𝐶)
41, 2, 33eqtr4g 2793 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  csymdif 4244
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-symdif 4245
This theorem is referenced by: (None)
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