Theorem eqnetrri 2270

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

Hypotheses

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

Assertion

Ref	Expression
eqnetrri	|- B =/= C

Proof of Theorem eqnetrri

Step	Hyp	Ref	Expression
1		eqnetrr.1	. . 3 |- A = B
2	1	eqcomi 2085	. 2 |- B = A
3		eqnetrr.2	. 2 |- A =/= C
4	2, 3	eqnetri 2268	1 |- B =/= C

Syntax hints:   = wceq 1284   =/= wne 2245

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-4 1440  ax-17 1459  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-ne 2246

This theorem is referenced by: (None)