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Theorem neeq2i 2527

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

**Hypothesis**
Ref	Expression
neeq1i.1	⊢ A = B

**Assertion**
Ref	Expression
neeq2i	⊢ (C ≠ A ↔ C ≠ B)

**Proof of Theorem neeq2i**
Step	Hyp	Ref	Expression
1		neeq1i.1	. 2 ⊢ A = B
2		neeq2 2525	. 2 ⊢ (A = B → (C ≠ A ↔ C ≠ B))
3	1, 2	ax-mp 8	1 ⊢ (C ≠ A ↔ C ≠ B)

Colors of variables: wff setvar class

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

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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 neeqtri 2537 nulnnn 4556 nchoicelem14 6302 nchoicelem17 6305