Theorem uneq1i 3415

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

Hypothesis

Ref	Expression
uneq1i.1	⊢ A = B

Assertion

Ref	Expression
uneq1i	⊢ (A ∪ C) = (B ∪ C)

Proof of Theorem uneq1i

Step	Hyp	Ref	Expression
1		uneq1i.1	. 2 ⊢ A = B
2		uneq1 3412	. 2 ⊢ (A = B → (A ∪ C) = (B ∪ C))
3	1, 2	ax-mp 5	1 ⊢ (A ∪ C) = (B ∪ C)

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:  un12  3422  unundi  3425  undif1  3626  dfif5  3675  tpcoma  3817  qdass  3820  qdassr  3821  tpidm12  3822  nnsucelrlem3  4427  phialllem2  4618  sbthlem1  6204  addccan2nclem2  6265