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  6558  djune  7268  omp1eomlem  7284  fodjum  7336  fodju0  7337  ismkvnex  7345  mkvprop  7348  omniwomnimkv  7357  pr2cv1  7391  3nelsucpw1  7442  xrltnr  10004  nltmnf  10013  xnn0xadd0  10092  fnpr2ob  13413  2lgslem3  15820  2lgslem4  15822  structiedg0val  15881  3dom  16523  2omap  16530  pwle2  16535  nninfalllem1  16546  nninfall  16547  nninfsellemeq  16552  trirec0xor  16585