Theorem ssun3 2192

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 2190	. 2 |- B (_ (B u. C)
2		sstr2 2068	. 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 2042   (_ wss 2044

This theorem is referenced by:  ssun 2203  pwundif 2824  xpsspw 3253

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217  ax-ext 1458

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1171  df-clab 1463  df-cleq 1468  df-clel 1471  df-v 1809  df-un 2047  df-in 2048  df-ss 2050

Copyright terms: Public domain