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Theorem ssnelpssd 3894
 Description: Subclass inclusion with one element of the superclass missing is proper subclass inclusion. Deduction form of ssnelpss 3893. (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 3893 . . 3
53, 4syl 16 . 2
61, 2, 5mp2and 679 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 369   wcel 1819   wss 3471   wpss 3472 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1614  df-cleq 2449  df-clel 2452  df-ne 2654  df-pss 3487 This theorem is referenced by:  isfin4-3  8712  canth4  9042  mrieqv2d  15056  symggen  16622  pgpfac1lem1  17252  pgpfaclem2  17260
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