Theorem nesymi 2393

Description: Inference associated with nesym 2392. (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 2392	. 2 |- ( A =/= B <-> -. B = A )
3	1, 2	mpbi 145	1 |- -. B = A

Syntax hints:   -. wn 3   = wceq 1353   =/= wne 2347

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 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-ne 2348

This theorem is referenced by:  frec0g  6398  djune  7077  omp1eomlem  7093  fodjum  7144  fodju0  7145  ismkvnex  7153  mkvprop  7156  omniwomnimkv  7165  3nelsucpw1  7233  xrltnr  9779  nltmnf  9788  xnn0xadd0  9867  fnpr2ob  12759  pwle2  14751  nninfalllem1  14760  nninfall  14761  nninfsellemeq  14766  trirec0xor  14796