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  6393  djune  7072  omp1eomlem  7088  fodjum  7139  fodju0  7140  ismkvnex  7148  mkvprop  7151  omniwomnimkv  7160  3nelsucpw1  7228  xrltnr  9773  nltmnf  9782  xnn0xadd0  9861  pwle2  14519  nninfalllem1  14528  nninfall  14529  nninfsellemeq  14534  trirec0xor  14564