Theorem nesymi 2413

Description: Inference associated with nesym 2412. (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 2412	. 2 |- ( A =/= B <-> -. B = A )
3	1, 2	mpbi 145	1 |- -. B = A

Syntax hints:   -. wn 3   = wceq 1364   =/= wne 2367

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 615  ax-in2 616  ax-5 1461  ax-gen 1463  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-ne 2368

This theorem is referenced by:  frec0g  6456  djune  7145  omp1eomlem  7161  fodjum  7213  fodju0  7214  ismkvnex  7222  mkvprop  7225  omniwomnimkv  7234  3nelsucpw1  7303  xrltnr  9856  nltmnf  9865  xnn0xadd0  9944  fnpr2ob  12993  2lgslem3  15352  2lgslem4  15354  pwle2  15653  nninfalllem1  15662  nninfall  15663  nninfsellemeq  15668  trirec0xor  15699