Theorem nesymi 2466

Description: Inference associated with nesym 2465. (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 2465	. 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐵 = 𝐴)
3	1, 2	mpbi 145	1 ⊢ ¬ 𝐵 = 𝐴

This proof depends on syntax axioms:  ¬ wn 3   = wceq 1402   ≠ wne 2420

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-5 1500  ax-gen 1502  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-ne 2421

This theorem is used by:  frec0g  6668  2omap  7318  djune  7418  omp1eomlem  7434  fodjum  7486  fodju0  7487  ismkvnex  7495  mkvprop  7498  omniwomnimkv  7507  pr2cv1  7541  3nelsucpw1  7593  xrltnr  10183  nltmnf  10192  xnn0xadd0  10271  ballotfilemi1  13247  fnpr2ob  13663  2lgslem3  16232  2lgslem4  16234  structiedg0val  16293  3dom  17030  pwle2  17040  exmidpeirce  17050  wexmiddifxylem  17057  nninfalllem1  17063  nninfall  17064  nninfsellemeq  17069  trirec0xor  17106