Theorem nesymi 2446

Description: Inference associated with nesym 2445. (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 2445	. 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐵 = 𝐴)
3	1, 2	mpbi 145	1 ⊢ ¬ 𝐵 = 𝐴

Syntax hints:  ¬ wn 3   = wceq 1395   ≠ wne 2400

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 617  ax-in2 618  ax-5 1493  ax-gen 1495  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-ne 2401

This theorem is referenced by:  frec0g  6554  djune  7261  omp1eomlem  7277  fodjum  7329  fodju0  7330  ismkvnex  7338  mkvprop  7341  omniwomnimkv  7350  pr2cv1  7384  3nelsucpw1  7435  xrltnr  9992  nltmnf  10001  xnn0xadd0  10080  fnpr2ob  13394  2lgslem3  15801  2lgslem4  15803  structiedg0val  15862  3dom  16465  2omap  16472  pwle2  16477  nninfalllem1  16488  nninfall  16489  nninfsellemeq  16494  trirec0xor  16527