Theorem neeqtri 2232

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 2221	. 2 |- ( A =/= B <-> A =/= C )
4	1, 3	mpbi 133	1 |- A =/= C

Syntax hints:   = wceq 1243   =/= wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206

This theorem is referenced by:  neeqtrri  2234