Theorem uneq2i 3416

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 3413	. 2 ⊢ (A = B → (C ∪ A) = (C ∪ B))
3	1, 2	ax-mp 5	1 ⊢ (C ∪ A) = (C ∪ B)

Syntax hints:   = wceq 1642   ∪ cun 3208

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 2479  df-v 2862  df-nin 3212  df-compl 3213  df-un 3215

This theorem is referenced by:  un4  3424  unundir  3426  difun2  3630  difdifdir  3638  dfif5  3675  qdass  3820  qdassr  3821  ssunpr  3869  iununi  4051  pw1eqadj  4333  nncaddccl  4420  ltfintrilem1  4466  ncfinraise  4482  tfinsuc  4499  nnadjoin  4521  sfindbl  4531  tfinnn  4535  fvsnun1  5448  sbthlem1  6204  leconnnc  6219  nchoicelem16  6305