Theorem nesymir 2852

Description: Inference associated with nesym 2850. (Contributed by BJ, 7-Jul-2018.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)

Hypothesis

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

Assertion

Ref	Expression
nesymir	|- B =/= A

Proof of Theorem nesymir

Step	Hyp	Ref	Expression
1		nesymir.1	. . 3 |- -. A = B
2	1	neir 2797	. 2 |- A =/= B
3	2	necomi 2848	1 |- B =/= A

Syntax hints:   -. wn 3   = wceq 1483   =/= wne 2794

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615  df-ne 2795

This theorem is referenced by:  relowlpssretop  33212