Theorem uneq2i 3415

Description: Inference adding union to the left in a class equality. (Contributed by NM, 30-Aug-1993.)

Hypothesis

Ref	Expression
uneq1i.1	⊢ A = B

Assertion

Ref	Expression
uneq2i	⊢ (C ∪ A) = (C ∪ B)

Proof of Theorem uneq2i

Step	Hyp	Ref	Expression
1		uneq1i.1	. 2 ⊢ A = B
2		uneq2 3412	. 2 ⊢ (A = B → (C ∪ A) = (C ∪ B))
3	1, 2	ax-mp 5	1 ⊢ (C ∪ A) = (C ∪ B)

Syntax hints:   = wceq 1642   ∪ cun 3207

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214

This theorem is referenced by:  un4  3423  unundir  3425  difun2  3629  difdifdir  3637  dfif5  3674  qdass  3819  qdassr  3820  ssunpr  3868  iununi  4050  pw1eqadj  4332  nncaddccl  4419  ltfintrilem1  4465  ncfinraise  4481  tfinsuc  4498  nnadjoin  4520  sfindbl  4530  tfinnn  4534  fvsnun1  5447  sbthlem1  6203  leconnnc  6218  nchoicelem16  6304