Theorem nesymir 2292

Description: Inference associated with nesym 2290. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
nesymir.1	|- -. A = B

Assertion

Ref	Expression
nesymir	|- B =/= A

Proof of Theorem nesymir

Step	Hyp	Ref	Expression
1		nesymir.1	. 2 |- -. A = B
2		nesym 2290	. 2 |- ( B =/= A <-> -. A = B )
3	1, 2	mpbir 144	1 |- B =/= A

Syntax hints:   -. wn 3   = wceq 1284   =/= wne 2245

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-ne 2246

This theorem is referenced by: (None)