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Mirrors > Home > ILE Home > Th. List > dif0 | Unicode version |
Description: The difference between a class and the empty set. Part of Exercise 4.4 of [Stoll] p. 16. (Contributed by NM, 17-Aug-2004.) |
Ref | Expression |
---|---|
dif0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difid 3401 | . . 3 | |
2 | 1 | difeq2i 3161 | . 2 |
3 | difdif 3171 | . 2 | |
4 | 2, 3 | eqtr3i 2140 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 cdif 3038 c0 3333 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rab 2402 df-v 2662 df-dif 3043 df-in 3047 df-ss 3054 df-nul 3334 |
This theorem is referenced by: disjdif2 3411 2oconcl 6304 diffifi 6756 undifdc 6780 difinfinf 6954 ismkvnex 6997 0cld 12208 exmid1stab 13122 |
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