Theorem neeq12i 2529

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 2528	. 2 |- (A =/= C <-> A =/= D)
3		neeq1i.1	. . 3 |- A = B
4	3	neeq1i 2527	. 2 |- (A =/= D <-> B =/= D)
5	2, 4	bitri 240	1 |- (A =/= C <-> B =/= D)

Syntax hints:   <-> wb 176   = wceq 1642   =/= wne 2517

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346  df-ne 2519

This theorem is referenced by:  3netr3g  2545  3netr4g  2546