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Theorem difsymssdifssd 4183
 Description: If the symmetric difference is contained in 𝐶, so is one of the differences. (Contributed by AV, 17-Aug-2022.)
Hypothesis
Ref Expression
difsymssdifssd.1 (𝜑 → (𝐴𝐵) ⊆ 𝐶)
Assertion
Ref Expression
difsymssdifssd (𝜑 → (𝐴𝐵) ⊆ 𝐶)

Proof of Theorem difsymssdifssd
StepHypRef Expression
1 difsssymdif 4182 . 2 (𝐴𝐵) ⊆ (𝐴𝐵)
2 difsymssdifssd.1 . 2 (𝜑 → (𝐴𝐵) ⊆ 𝐶)
31, 2sstrid 3928 1 (𝜑 → (𝐴𝐵) ⊆ 𝐶)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∖ cdif 3880   ⊆ wss 3883   △ csymdif 4171 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-un 3888  df-in 3890  df-ss 3900  df-symdif 4172 This theorem is referenced by:  mbfeqalem1  24286
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