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)

Syntax hints:   → wi 4   ≠ 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-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