Theorem equncomi 3217

Description: Inference form of equncom 3216. (Contributed by Alan Sare, 18-Feb-2012.)

Hypothesis

Ref	Expression
equncomi.1	|- A = ( B u. C )

Assertion

Ref	Expression
equncomi	|- A = ( C u. B )

Proof of Theorem equncomi

Step	Hyp	Ref	Expression
1		equncomi.1	. 2 |- A = ( B u. C )
2		equncom 3216	. 2 |- ( A = ( B u. C ) <-> A = ( C u. B ) )
3	1, 2	mpbi 144	1 |- A = ( C u. B )

Syntax hints:   = wceq 1331   u. cun 3064

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070

This theorem is referenced by:  disjssun  3421  difprsn1  3654  unidmrn  5066  phplem1  6739  djucomen  7065