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Theorem difsymssdifssd 4227
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 4226 . 2 (𝐴𝐵) ⊆ (𝐴𝐵)
2 difsymssdifssd.1 . 2 (𝜑 → (𝐴𝐵) ⊆ 𝐶)
31, 2sstrid 3975 1 (𝜑 → (𝐴𝐵) ⊆ 𝐶)
Colors of variables: wff setvar class
Syntax hints:  wi 4  cdif 3930  wss 3933  csymdif 4215
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-un 3938  df-in 3940  df-ss 3949  df-symdif 4216
This theorem is referenced by:  mbfeqalem1  24169
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