Theorem neeq1i 2374

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 2372	. 2 |- ( A = B -> ( A =/= C <-> B =/= C ) )
3	1, 2	ax-mp 5	1 |- ( A =/= C <-> B =/= C )

Syntax hints:   <-> wb 105   = wceq 1363   =/= wne 2359

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 615  ax-in2 616  ax-5 1457  ax-gen 1459  ax-4 1520  ax-17 1536  ax-ext 2170

This theorem depends on definitions:  df-bi 117  df-cleq 2181  df-ne 2360

This theorem is referenced by:  neeq12i  2376  eqnetri  2382  eqnetrrid  2390  rabn0r  3463