Theorem neeqtrri 2311

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

Hypotheses

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

Assertion

Ref	Expression
neeqtrri	|- A =/= C

Proof of Theorem neeqtrri

Step	Hyp	Ref	Expression
1		neeqtrr.1	. 2 |- A =/= B
2		neeqtrr.2	. . 3 |- C = B
3	2	eqcomi 2119	. 2 |- B = C
4	1, 3	neeqtri 2309	1 |- A =/= C

Syntax hints:   = wceq 1314   =/= wne 2282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-4 1470  ax-17 1489  ax-ext 2097

This theorem depends on definitions:  df-bi 116  df-cleq 2108  df-ne 2283

This theorem is referenced by:  pnfnemnf  7744  basendxnplusgndx  11908  plusgndxnmulrndx  11915  basendxnmulrndx  11916