Theorem equncomi 4130

Description: Inference form of equncom 4129. equncomi 4130 was automatically derived from equncomiVD 41196 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 4129	. 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵))
3	1, 2	mpbi 232	1 ⊢ 𝐴 = (𝐶 ∪ 𝐵)

Syntax hints:   = wceq 1533   ∪ cun 3933

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-v 3496  df-un 3940

This theorem is referenced by:  disjssun  4416  difprsn1  4726  unidmrn  6124  phplem1  8690  djucomen  9597  ackbij1lem14  9649  ltxrlt  10705  ruclem6  15582  ruclem7  15583  i1f1  24285  vtxdgoddnumeven  27329  subfacp1lem1  32421  lindsenlbs  34881  poimirlem6  34892  poimirlem7  34893  poimirlem16  34902  poimirlem17  34903  pwfi2f1o  39689  cnvrcl0  39978  iunrelexp0  40040  dfrtrcl4  40076  cotrclrcl  40080  dffrege76  40278  sucidALTVD  41197  sucidALT  41198