Theorem eqnetrri 2865

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 2631	. 2 |- B = A
3		eqnetrr.2	. 2 |- A =/= C
4	2, 3	eqnetri 2864	1 |- B =/= C

Syntax hints:   = wceq 1483   =/= wne 2794

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615  df-ne 2795

This theorem is referenced by:  ballotlemii  30565  bj-2upln1upl  33012  wallispilem4  40285