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Mirrors > Home > ILE Home > Th. List > ssneldd | Unicode version |
Description: If an element is not in a class, it is also not in a subclass of that class. Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
ssneld.1 | |
ssneldd.2 |
Ref | Expression |
---|---|
ssneldd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssneldd.2 | . 2 | |
2 | ssneld.1 | . . 3 | |
3 | 2 | ssneld 3094 | . 2 |
4 | 1, 3 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wcel 1480 wss 3066 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-in 3072 df-ss 3079 |
This theorem is referenced by: 0nelrel 4580 addnqprlemfl 7360 addnqprlemfu 7361 mulnqprlemfl 7376 mulnqprlemfu 7377 cauappcvgprlemladdru 7457 |
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