Theorem equncomi 4156

Description: Inference form of equncom 4155. equncomi 4156 was automatically derived from equncomiVD 43630 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 4155	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	1, 2	mpbi 229	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

Syntax hints:   = wceq 1542   ∪ cun 3947

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3954

This theorem is referenced by:  disjssun  4468  difprsn1  4804  unidmrn  6279  phplem1OLD  9217  djucomen  10172  ackbij1lem14  10228  ltxrlt  11284  ruclem6  16178  ruclem7  16179  i1f1  25207  vtxdgoddnumeven  28810  subfacp1lem1  34170  lindsenlbs  36483  poimirlem6  36494  poimirlem7  36495  poimirlem16  36504  poimirlem17  36505  pwfi2f1o  41838  cnvrcl0  42376  iunrelexp0  42453  dfrtrcl4  42489  cotrclrcl  42493  dffrege76  42690  sucidALTVD  43631  sucidALT  43632