Theorem ssun4 2192

Description: Subclass law for union of classes.

Assertion

Ref	Expression
ssun4	|- (A (_ B -> A (_ (C u. B))

Proof of Theorem ssun4

Step	Hyp	Ref	Expression
1		ssun2 2190	. 2 |- B (_ (C u. B)
2		sstr2 2067	. 2 |- (A (_ B -> (B (_ (C u. B) -> A (_ (C u. B)))
3	1, 2	mpi 44	1 |- (A (_ B -> A (_ (C u. B))

Syntax hints:   -> wi 3   u. cun 2041   (_ wss 2043

This theorem is referenced by:  ssun 2202  xpsspw 3252

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808  df-un 2046  df-in 2047  df-ss 2049

Copyright terms: Public domain