Theorem neeq1i 2297

Description: Inference for inequality. (Contributed by NM, 29-Apr-2005.)

Hypothesis

Ref	Expression
neeq1i.1	|- A = B

Assertion

Ref	Expression
neeq1i	|- ( A =/= C <-> B =/= C )

Proof of Theorem neeq1i

Step	Hyp	Ref	Expression
1		neeq1i.1	. 2 |- A = B
2		neeq1 2295	. 2 |- ( A = B -> ( A =/= C <-> B =/= C ) )
3	1, 2	ax-mp 7	1 |- ( A =/= C <-> B =/= C )

Syntax hints:   <-> wb 104   = wceq 1314   =/= wne 2282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-4 1470  ax-17 1489  ax-ext 2097

This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2283

This theorem is referenced by:  neeq12i  2299  eqnetri  2305  syl5eqner  2313  rabn0r  3355