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  6400  djune  7079  omp1eomlem  7095  fodjum  7146  fodju0  7147  ismkvnex  7155  mkvprop  7158  omniwomnimkv  7167  3nelsucpw1  7235  xrltnr  9781  nltmnf  9790  xnn0xadd0  9869  fnpr2ob  12764  pwle2  14787  nninfalllem1  14796  nninfall  14797  nninfsellemeq  14802  trirec0xor  14832