Theorem inss 3726

Description: Inclusion of an intersection of two classes. (Contributed by NM, 30-Oct-2014.)

Assertion

Ref	Expression
inss

Proof of Theorem inss

Step	Hyp	Ref	Expression
1		ssinss1 3725	. 2
2		incom 3690	. . 3
3		ssinss1 3725	. . 3
4	2, 3	syl5eqss 3547	. 2
5	1, 4	jaoi 379	1

Syntax hints:  ->wi 4  \/wo 368  i^icin 3474  C_wss 3475

This theorem is referenced by:  pmatcoe1fsupp  19202  ppttop  19508  inindif  27414  icccncfext  31690

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-in 3482  df-ss 3489