Theorem nesymir 2252

Description: Inference associated with nesym 2250. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
nesymir.1	⊢ ¬ 𝐴 = 𝐵

Assertion

Ref	Expression
nesymir	⊢ 𝐵 ≠ 𝐴

Proof of Theorem nesymir

Step	Hyp	Ref	Expression
1		nesymir.1	. 2 ⊢ ¬ 𝐴 = 𝐵
2		nesym 2250	. 2 ⊢ (𝐵 ≠ 𝐴 ↔ ¬ 𝐴 = 𝐵)
3	1, 2	mpbir 134	1 ⊢ 𝐵 ≠ 𝐴

Syntax hints:  ¬ wn 3   = wceq 1243   ≠ wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206

This theorem is referenced by: (None)