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Theorem necomd 2599

Description: Deduction from commutative law for inequality. (Contributed by NM, 12-Feb-2008.)

**Hypothesis**
Ref	Expression
necomd.1	⊢ (φ → A ≠ B)

**Assertion**
Ref	Expression
necomd	⊢ (φ → B ≠ A)

**Proof of Theorem necomd**
Step	Hyp	Ref	Expression
1		necomd.1	. 2 ⊢ (φ → A ≠ B)
2		necom 2597	. 2 ⊢ (A ≠ B ↔ B ≠ A)
3	1, 2	sylib 188	1 ⊢ (φ → B ≠ A)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ≠ 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-ext 2334

This theorem depends on definitions: df-bi 177 df-cleq 2346 df-ne 2518

This theorem is referenced by: difsnb 3850 vfinncvntnn 4548 vfinncvntsp 4549 nchoicelem12 6300 nchoicelem17 6305