Theorem ssun3 2195

Description: Subclass law for union of classes.

Assertion

Ref	Expression
ssun3	|- (A (_ B -> A (_ (B u. C))

Proof of Theorem ssun3

Step	Hyp	Ref	Expression
1		ssun1 2193	. 2 |- B (_ (B u. C)
2		sstr2 2071	. 2 |- (A (_ B -> (B (_ (B u. C) -> A (_ (B u. C)))
3	1, 2	mpi 44	1 |- (A (_ B -> A (_ (B u. C))

Syntax hints:   -> wi 3   u. cun 2045   (_ wss 2047

This theorem is referenced by:  ssun 2206  pwundif 2828  xpsspw 3257

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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