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Theorem ssnelpssd 3891
Description: Subclass inclusion with one element of the superclass missing is proper subclass inclusion. Deduction form of ssnelpss 3890. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
ssnelpssd.1
ssnelpssd.2
ssnelpssd.3
Assertion
Ref Expression
ssnelpssd

Proof of Theorem ssnelpssd
StepHypRef Expression
1 ssnelpssd.2 . 2
2 ssnelpssd.3 . 2
3 ssnelpssd.1 . . 3
4 ssnelpss 3890 . . 3
53, 4syl 16 . 2
61, 2, 5mp2and 679 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  /\wa 369  e.wcel 1818  C_wss 3475  C.wpss 3476
This theorem is referenced by:  isfin4-3  8716  canth4  9046  mrieqv2d  15036  symggen  16495  pgpfac1lem1  17125  pgpfaclem2  17133
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-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-cleq 2449  df-clel 2452  df-ne 2654  df-pss 3491
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