Theorem nesymi 2393

Description: Inference associated with nesym 2392. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
nesymi.1	⊢ 𝐴 ≠ 𝐵

Assertion

Ref	Expression
nesymi	⊢ ¬ 𝐵 = 𝐴

Proof of Theorem nesymi

Step	Hyp	Ref	Expression
1		nesymi.1	. 2 ⊢ 𝐴 ≠ 𝐵
2		nesym 2392	. 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐵 = 𝐴)
3	1, 2	mpbi 145	1 ⊢ ¬ 𝐵 = 𝐴

Syntax hints:  ¬ wn 3   = wceq 1353   ≠ wne 2347

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-ne 2348

This theorem is referenced by:  frec0g  6397  djune  7076  omp1eomlem  7092  fodjum  7143  fodju0  7144  ismkvnex  7152  mkvprop  7155  omniwomnimkv  7164  3nelsucpw1  7232  xrltnr  9777  nltmnf  9786  xnn0xadd0  9865  pwle2  14630  nninfalllem1  14639  nninfall  14640  nninfsellemeq  14645  trirec0xor  14675