Theorem ssun 2206

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 2195	. 2 |- (A (_ B -> A (_ (B u. C))
2		ssun4 2196	. 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 2045   (_ wss 2047

This theorem is referenced by:  pwunss 2826  pwssun 2827  ordssun 3079

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-un 2050  df-in 2051  df-ss 2053

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