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Metamath Proof Explorer

Theorem eqnetrri

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012)

Ref Expression
Hypotheses eqnetrr.1 ⊢ A = B
eqnetrr.2 ⊢ A ≠ C
Assertion eqnetrri ⊢ B ≠ C

Proof

Step Hyp Ref Expression
1 eqnetrr.1 ⊢ A = B
2 eqnetrr.2 ⊢ A ≠ C
3 1 eqcomi ⊢ B = A
4 3 2 eqnetri ⊢ B ≠ C