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Theorem ineqcom 35385
Description: Two ways of saying that two classes are disjoint (when 𝐶 = ∅: ((𝐴𝐵) = ∅ ↔ (𝐵𝐴) = ∅)). (Contributed by Peter Mazsa, 22-Mar-2017.)
Assertion
Ref Expression
ineqcom ((𝐴𝐵) = 𝐶 ↔ (𝐵𝐴) = 𝐶)

Proof of Theorem ineqcom
StepHypRef Expression
1 incom 4175 . 2 (𝐴𝐵) = (𝐵𝐴)
21eqeq1i 2823 1 ((𝐴𝐵) = 𝐶 ↔ (𝐵𝐴) = 𝐶)
Colors of variables: wff setvar class
Syntax hints:  wb 207   = wceq 1528  cin 3932
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-9 2115  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1531  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-rab 3144  df-in 3940
This theorem is referenced by:  ineqcomi  35386
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