Theorem nssne2 3560

Description: Two classes are different if they are not subclasses of the same class. (Contributed by NM, 23-Apr-2015.)

Assertion

Ref	Expression
nssne2

Proof of Theorem nssne2

Step	Hyp	Ref	Expression
1		sseq1 3524	. . . 4
2	1	biimpcd 224	. . 3
3	2	necon3bd 2669	. 2
4	3	imp 429	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  =wceq 1395  =/=wne 2652  C_wss 3475

This theorem is referenced by:  atcvatlem  27304  mdsymlem3  27324  disjdifprg  27436  mapdh6aN  37462  mapdh8e  37511  hdmap1l6a  37537

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-ne 2654  df-in 3482  df-ss 3489