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Theorem symdifeq2 4207
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 4206 . 2 (𝐴 = 𝐵 → (𝐴𝐶) = (𝐵𝐶))
2 symdifcom 4205 . 2 (𝐶𝐴) = (𝐴𝐶)
3 symdifcom 4205 . 2 (𝐶𝐵) = (𝐵𝐶)
41, 2, 33eqtr4g 2884 1 (𝐴 = 𝐵 → (𝐶𝐴) = (𝐶𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538  csymdif 4203
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-rab 3142  df-v 3482  df-dif 3922  df-un 3924  df-symdif 4204
This theorem is referenced by: (None)
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