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Mirrors > Home > ILE Home > Th. List > sseq0 | Unicode version |
Description: A subclass of an empty class is empty. (Contributed by NM, 7-Mar-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
sseq0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq2 3152 | . . 3 | |
2 | ss0 3434 | . . 3 | |
3 | 1, 2 | syl6bi 162 | . 2 |
4 | 3 | impcom 124 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wss 3102 c0 3394 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-in 3108 df-ss 3115 df-nul 3395 |
This theorem is referenced by: ssn0 3436 ssdifin0 3475 fieq0 6920 fisumss 11289 strleund 12278 strleun 12279 |
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