Theorem equncomi 4107

Description: Inference form of equncom 4106. equncomi 4107 was automatically derived from equncomiVD 45692 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 4106	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	1, 2	mpbi 233	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

This proof depends on syntax axioms:   = wceq 1570   ∪ cun 3897

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-un 3904

This theorem is used by:  disjssun  4421  difprsn1  4763  unidmrn  6277  djucomen  10181  ackbij1lem14  10235  ltxrlt  11305  ruclem6  16324  ruclem7  16325  lindsenlbs  22065  i1f1  25919  vtxdgoddnumeven  30014  subfacp1lem1  35759  poimirlem6  38376  poimirlem7  38377  poimirlem16  38386  poimirlem17  38387  pwfi2f1o  43938  cnvrcl0  44466  iunrelexp0  44543  dfrtrcl4  44579  cotrclrcl  44583  dffrege76  44780  sucidALTVD  45693  sucidALT  45694  usgrexmpl2edg  48946