Theorem unss12 1630

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 1627	. . 3 |- (A (_ B -> (A u. C) (_ (B u. C))
2	1	adantr 306	. 2 |- ((A (_ B /\ C (_ D) -> (A u. C) (_ (B u. C))
3		unss2 1629	. . 3 |- (C (_ D -> (B u. C) (_ (B u. D))
4	3	adantl 305	. 2 |- ((A (_ B /\ C (_ D) -> (B u. C) (_ (B u. D))
5	2, 4	sstrd 1513	1 |- ((A (_ B /\ C (_ D) -> (A u. C) (_ (B u. D))

Syntax hints:   -> wi 2   /\ wa 196   u. cun 1485   (_ wss 1487

This theorem is referenced by:  pwssun 1917  fun 2763  undom 3342  spanun 5450  sshhococ 5451

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-un 1490  df-in 1491  df-ss 1492

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