Theorem intssOLD 4308

Description: Intersection of subclasses. (Contributed by NM, 14-Oct-1999.) Obsolete version of intss 4307 as of 25-Mar-2020. (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
intssOLD

Proof of Theorem intssOLD

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		imim1 76	. . . . 5
2	1	al2imi 1636	. . . 4
3		vex 3112	. . . . 5
4	3	elint 4292	. . . 4
5	3	elint 4292	. . . 4
6	2, 4, 5	3imtr4g 270	. . 3
7	6	alrimiv 1719	. 2
8		dfss2 3492	. 2
9		dfss2 3492	. 2
10	7, 8, 9	3imtr4i 266	1

Syntax hints:  ->wi 4  A.wal 1393  e.wcel 1818  C_wss 3475  |^|cint 4286

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-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  df-int 4287