Theorem pssnel 3893

Description: A proper subclass has a member in one argument that's not in both. (Contributed by NM, 29-Feb-1996.)

Assertion

Ref	Expression
pssnel

Distinct variable groups:   ,   ,

Proof of Theorem pssnel

Step	Hyp	Ref	Expression
1		pssdif 3889	. . 3
2		n0 3794	. . 3
3	1, 2	sylib 196	. 2
4		eldif 3485	. . 3
5	4	exbii 1667	. 2
6	3, 5	sylib 196	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  E.wex 1612  e.wcel 1818  =/=wne 2652  \cdif 3472  C.wpss 3476  c0 3784

This theorem is referenced by:  php  7721  php3  7723  pssnn  7758  inf3lem2  8067  infpssr  8709  ssfin4  8711  genpnnp  9404  ltexprlem1  9435  reclem2pr  9447  mrieqv2d  15036  lbspss  17728  lsmcv  17787  lidlnz  17876  obslbs  18761  nmoid  21249  spansncvi  26570  lsat0cv  34758  osumcllem11N  35690  pexmidlem8N  35701

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-ne 2654  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-pss 3491  df-nul 3785