Theorem equncomi 3083

Description: Inference form of equncom 3082. (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 3082	. 2 |- (A = (B u. C) <-> A = ( C u. B))
3	1, 2	mpbi 133	1 |- A = ( C u. B)

Syntax hints:   = wceq 1242   u. cun 2909

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916

This theorem is referenced by:  disjssun  3279  difprsn1  3494  unidmrn  4793