Theorem neeq1i 2526

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 2524	. 2 |- (A = B -> (A =/= C <-> B =/= C))
3	1, 2	ax-mp 8	1 |- (A =/= C <-> B =/= C)

Syntax hints:   <-> wb 176   = wceq 1642   =/= wne 2516

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346  df-ne 2518

This theorem is referenced by:  neeq12i  2528  eqnetri  2533  syl5eqner  2541  rabn0  3570  ltfinirr  4457  evenodddisj  4516