Theorem neeqtri 2387

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 2376	. 2 |- ( A =/= B <-> A =/= C )
4	1, 3	mpbi 145	1 |- A =/= C

Syntax hints:   = wceq 1364   =/= wne 2360

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 1458  ax-gen 1460  ax-4 1521  ax-17 1537  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-cleq 2182  df-ne 2361

This theorem is referenced by:  neeqtrri  2389