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Theorem difsssymdif 4179
 Description: The symmetric difference contains one of the differences. (Proposed by BJ, 18-Aug-2022.) (Contributed by AV, 19-Aug-2022.)
Assertion
Ref Expression
difsssymdif (𝐴𝐵) ⊆ (𝐴𝐵)

Proof of Theorem difsssymdif
StepHypRef Expression
1 ssun1 4099 . 2 (𝐴𝐵) ⊆ ((𝐴𝐵) ∪ (𝐵𝐴))
2 df-symdif 4169 . 2 (𝐴𝐵) = ((𝐴𝐵) ∪ (𝐵𝐴))
31, 2sseqtrri 3952 1 (𝐴𝐵) ⊆ (𝐴𝐵)
 Colors of variables: wff setvar class Syntax hints:   ∖ cdif 3878   ∪ cun 3879   ⊆ wss 3881   △ csymdif 4168 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 3443  df-un 3886  df-in 3888  df-ss 3898  df-symdif 4169 This theorem is referenced by:  difsymssdifssd  4180
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