Theorem equncomi 4123

Description: Inference form of equncom 4122. equncomi 4123 was automatically derived from equncomiVD 44858 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 4122	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	1, 2	mpbi 230	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

Syntax hints:   = wceq 1540   ∪ cun 3912

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-un 3919

This theorem is referenced by:  disjssun  4431  difprsn1  4764  unidmrn  6252  djucomen  10131  ackbij1lem14  10185  ltxrlt  11244  ruclem6  16203  ruclem7  16204  i1f1  25591  vtxdgoddnumeven  29481  subfacp1lem1  35166  lindsenlbs  37609  poimirlem6  37620  poimirlem7  37621  poimirlem16  37630  poimirlem17  37631  pwfi2f1o  43085  cnvrcl0  43614  iunrelexp0  43691  dfrtrcl4  43727  cotrclrcl  43731  dffrege76  43928  sucidALTVD  44859  sucidALT  44860  usgrexmpl2edg  48020