Theorem equncomi 3737

Description: Inference form of equncom 3736. equncomi 3737 was automatically derived from equncomiVD 38585 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 3736	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	1, 2	mpbi 220	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

Syntax hints:   = wceq 1480   ∪ cun 3553

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-un 3560

This theorem is referenced by:  disjssun  4008  difprsn1  4299  unidmrn  5624  phplem1  8083  ackbij1lem14  8999  ltxrlt  10052  ruclem6  14889  ruclem7  14890  i1f1  23363  subfacp1lem1  30866  lindsenlbs  33033  poimirlem6  33044  poimirlem7  33045  poimirlem16  33054  poimirlem17  33055  pwfi2f1o  37143  cnvrcl0  37410  iunrelexp0  37472  dfrtrcl4  37508  cotrclrcl  37512  dffrege76  37712  sucidALTVD  38586  sucidALT  38587