Theorem neeq1i 2526

Description: Inference for inequality. (Contributed by NM, 29-Apr-2005.)

Hypothesis

Ref	Expression
neeq1i.1	⊢ A = B

Assertion

Ref	Expression
neeq1i	⊢ (A ≠ C ↔ B ≠ C)

Proof of Theorem neeq1i

Step	Hyp	Ref	Expression
1		neeq1i.1	. 2 ⊢ A = B
2		neeq1 2524	. 2 ⊢ (A = B → (A ≠ C ↔ B ≠ C))
3	1, 2	ax-mp 5	1 ⊢ (A ≠ C ↔ B ≠ C)

Syntax hints:   ↔ wb 176   = wceq 1642   ≠ wne 2516

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 2518

This theorem is referenced by:  neeq12i  2528  eqnetri  2533  syl5eqner  2541  rabn0  3570  ltfinirr  4457  evenodddisj  4516