Theorem ssun 2209

Description: A condition that implies inclusion in the union of two classes.

Assertion

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

Proof of Theorem ssun

Step	Hyp	Ref	Expression
1		ssun3 2198	. 2 |- (A (_ B -> A (_ (B u. C))
2		ssun4 2199	. 2 |- (A (_ C -> A (_ (B u. C))
3	1, 2	jaoi 341	1 |- ((A (_ B \/ A (_ C) -> A (_ (B u. C))

Syntax hints:   -> wi 3   \/ wo 222   u. cun 2048   (_ wss 2050

This theorem is referenced by:  pwunss 2832  pwssun 2833  ordssun 3085

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-v 1815  df-un 2053  df-in 2054  df-ss 2056

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