Theorem equncomi 4113

Description: Inference form of equncom 4112. equncomi 4113 was automatically derived from equncomiVD 44845 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 4112	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	1, 2	mpbi 230	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

Syntax hints:   = wceq 1540   ∪ cun 3903

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 3440  df-un 3910

This theorem is referenced by:  disjssun  4421  difprsn1  4754  unidmrn  6231  djucomen  10091  ackbij1lem14  10145  ltxrlt  11204  ruclem6  16162  ruclem7  16163  i1f1  25607  vtxdgoddnumeven  29517  subfacp1lem1  35154  lindsenlbs  37597  poimirlem6  37608  poimirlem7  37609  poimirlem16  37618  poimirlem17  37619  pwfi2f1o  43072  cnvrcl0  43601  iunrelexp0  43678  dfrtrcl4  43714  cotrclrcl  43718  dffrege76  43915  sucidALTVD  44846  sucidALT  44847  usgrexmpl2edg  48017