Theorem ssun 3338

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 3324	. 2 |- ( A C_ B -> A C_ ( B u. C ) )
2		ssun4 3325	. 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 3151   C_ wss 3153

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-in 3159  df-ss 3166

This theorem is referenced by:  pwunss  4314  pwssunim  4315