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  6541  djune  7241  omp1eomlem  7257  fodjum  7309  fodju0  7310  ismkvnex  7318  mkvprop  7321  omniwomnimkv  7330  pr2cv1  7364  3nelsucpw1  7415  xrltnr  9971  nltmnf  9980  xnn0xadd0  10059  fnpr2ob  13368  2lgslem3  15774  2lgslem4  15776  structiedg0val  15835  2omap  16318  pwle2  16323  nninfalllem1  16333  nninfall  16334  nninfsellemeq  16339  trirec0xor  16372