Theorem neeqtri 2363

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)

Hypotheses

Ref	Expression
neeqtr.1	|- A =/= B
neeqtr.2	|- B = C

Assertion

Ref	Expression
neeqtri	|- A =/= C

Proof of Theorem neeqtri

Step	Hyp	Ref	Expression
1		neeqtr.1	. 2 |- A =/= B
2		neeqtr.2	. . 3 |- B = C
3	2	neeq2i 2352	. 2 |- ( A =/= B <-> A =/= C )
4	1, 3	mpbi 144	1 |- A =/= C

Syntax hints:   = wceq 1343   =/= wne 2336

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 1435  ax-gen 1437  ax-4 1498  ax-17 1514  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-cleq 2158  df-ne 2337

This theorem is referenced by:  neeqtrri  2365