Theorem ssun 3328

Description: A condition that implies inclusion in the union of two classes. (Contributed by NM, 23-Nov-2003.)

Assertion

Ref	Expression
ssun	|- ( ( A C_ B \/ A C_ C ) -> A C_ ( B u. C ) )

Proof of Theorem ssun

Step	Hyp	Ref	Expression
1		ssun3 3314	. 2 |- ( A C_ B -> A C_ ( B u. C ) )
2		ssun4 3315	. 2 |- ( A C_ C -> A C_ ( B u. C ) )
3	1, 2	jaoi 717	1 |- ( ( A C_ B \/ A C_ C ) -> A C_ ( B u. C ) )

Syntax hints:   -> wi 4   \/ wo 709   u. cun 3141   C_ wss 3143

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-v 2753  df-un 3147  df-in 3149  df-ss 3156

This theorem is referenced by:  pwunss  4297  pwssunim  4298