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Mirrors > Home > NFE Home > Th. List > ssnelpss | Unicode version |
Description: A subclass missing a member is a proper subclass. (Contributed by NM, 12-Jan-2002.) |
Ref | Expression |
---|---|
ssnelpss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nelneq2 2452 |
. . 3
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2 | eqcom 2355 |
. . 3
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3 | 1, 2 | sylnib 295 |
. 2
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4 | dfpss2 3355 |
. . 3
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5 | 4 | baibr 872 |
. 2
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6 | 3, 5 | syl5ib 210 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-cleq 2346 df-clel 2349 df-ne 2519 df-pss 3262 |
This theorem is referenced by: ssnelpssd 3615 |
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