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