Theorem unss12 2205

Description: Subclass law for union of classes.

Assertion

Ref	Expression
unss12	|- ((A (_ B /\ C (_ D) -> (A u. C) (_ (B u. D))

Proof of Theorem unss12

Step	Hyp	Ref	Expression
1		unss1 2202	. 2 |- (A (_ B -> (A u. C) (_ (B u. C))
2		unss2 2204	. 2 |- (C (_ D -> (B u. C) (_ (B u. D))
3	1, 2	sylan9ss 2078	1 |- ((A (_ B /\ C (_ D) -> (A u. C) (_ (B u. D))

Syntax hints:   -> wi 3   /\ wa 223   u. cun 2048   (_ wss 2050

This theorem is referenced by:  pwssun 2833  fun 3647  undom 4444  spanun 9462  sshhococ 9464

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

Copyright terms: Public domain