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Theorem ineqcomi 35930
 Description: Disjointness inference (when 𝐶 = ∅), inference form of ineqcom 35929. (Contributed by Peter Mazsa, 26-Mar-2017.)
Hypothesis
Ref Expression
ineqcomi.1 (𝐴𝐵) = 𝐶
Assertion
Ref Expression
ineqcomi (𝐵𝐴) = 𝐶

Proof of Theorem ineqcomi
StepHypRef Expression
1 ineqcomi.1 . 2 (𝐴𝐵) = 𝐶
2 ineqcom 35929 . 2 ((𝐴𝐵) = 𝐶 ↔ (𝐵𝐴) = 𝐶)
31, 2mpbi 233 1 (𝐵𝐴) = 𝐶
 Colors of variables: wff setvar class Syntax hints:   = wceq 1539   ∩ cin 3853 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-9 2122  ax-ext 2730 This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-rab 3077  df-in 3861 This theorem is referenced by:  inres2  35931
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