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Theorem ssnelpssd 3692
 Description: Subclass inclusion with one element of the superclass missing is proper subclass inclusion. Deduction form of ssnelpss 3691. (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 3691 . . 3
53, 4syl 16 . 2
61, 2, 5mp2and 661 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359   wcel 1725   wss 3320   wpss 3321 This theorem is referenced by:  isfin4-3  8195  canth4  8522  mrieqv2d  13864  pgpfac1lem1  15632  pgpfaclem2  15640  symggen  27388 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-cleq 2429  df-clel 2432  df-ne 2601  df-pss 3336
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