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Theorem ssnelpssd 3290
 Description: Subclass inclusion with one element of the superclass missing is proper subclass inclusion. Deduction form of ssnelpss 3289. (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 3289 . . 3
53, 4syl 14 . 2
61, 2, 5mp2and 409 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wcel 1393   wss 2917   wpss 2918 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-clel 2036  df-ne 2206  df-pss 2933 This theorem is referenced by: (None)
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