Theorem equncomi 3410

Description: Inference form of equncom 3409. equncomi 3410 was automatically derived from equncomiVD in set.mm using the tools program translate_without_overwriting.cmd and minimizing. (Contributed by Alan Sare, 18-Feb-2012.)

Hypothesis

Ref	Expression
equncomi.1	⊢ A = (B ∪ C)

Assertion

Ref	Expression
equncomi	⊢ A = (C ∪ B)

Proof of Theorem equncomi

Step	Hyp	Ref	Expression
1		equncomi.1	. 2 ⊢ A = (B ∪ C)
2		equncom 3409	. 2 ⊢ (A = (B ∪ C) ↔ A = (C ∪ B))
3	1, 2	mpbi 199	1 ⊢ A = (C ∪ B)

Syntax hints:   = wceq 1642   ∪ cun 3207

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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214

This theorem is referenced by:  disjssun  3608  difprsn1  3847