Theorem ssun 3356

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 3342	. 2 |- ( A C_ B -> A C_ ( B u. C ) )
2		ssun4 3343	. 2 |- ( A C_ C -> A C_ ( B u. C ) )
3	1, 2	jaoi 718	1 |- ( ( A C_ B \/ A C_ C ) -> A C_ ( B u. C ) )

Syntax hints:   -> wi 4   \/ wo 710   u. cun 3168   C_ wss 3170

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-un 3174  df-in 3176  df-ss 3183

This theorem is referenced by:  pwunss  4338  pwssunim  4339