Theorem neeq12i 2351

Description: Inference for inequality. (Contributed by NM, 24-Jul-2012.)

Hypotheses

Ref	Expression
neeq1i.1	|- A = B
neeq12i.2	|- C = D

Assertion

Ref	Expression
neeq12i	|- ( A =/= C <-> B =/= D )

Proof of Theorem neeq12i

Step	Hyp	Ref	Expression
1		neeq12i.2	. . 3 |- C = D
2	1	neeq2i 2350	. 2 |- ( A =/= C <-> A =/= D )
3		neeq1i.1	. . 3 |- A = B
4	3	neeq1i 2349	. 2 |- ( A =/= D <-> B =/= D )
5	2, 4	bitri 183	1 |- ( A =/= C <-> B =/= D )

Syntax hints:   <-> wb 104   = wceq 1342   =/= wne 2334

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1434  ax-gen 1436  ax-4 1497  ax-17 1513  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-cleq 2157  df-ne 2335

This theorem is referenced by:  3netr3g  2368  3netr4g  2369  setsmsbasg  13020  setsmsdsg  13021