Theorem neeq1i 2342

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 2340	. 2 |- ( A = B -> ( A =/= C <-> B =/= C ) )
3	1, 2	ax-mp 5	1 |- ( A =/= C <-> B =/= C )

Syntax hints:   <-> wb 104   = wceq 1335   =/= wne 2327

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1427  ax-gen 1429  ax-4 1490  ax-17 1506  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-cleq 2150  df-ne 2328

This theorem is referenced by:  neeq12i  2344  eqnetri  2350  eqnetrrid  2358  rabn0r  3421