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Mirrors > Home > ILE Home > Th. List > co02 | Unicode version |
Description: Composition with the empty set. Theorem 20 of [Suppes] p. 63. (Contributed by NM, 24-Apr-2004.) |
Ref | Expression |
---|---|
co02 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relco 5007 | . 2 | |
2 | rel0 4634 | . 2 | |
3 | noel 3337 | . . . . . . 7 | |
4 | df-br 3900 | . . . . . . 7 | |
5 | 3, 4 | mtbir 645 | . . . . . 6 |
6 | 5 | intnanr 900 | . . . . 5 |
7 | 6 | nex 1461 | . . . 4 |
8 | vex 2663 | . . . . 5 | |
9 | vex 2663 | . . . . 5 | |
10 | 8, 9 | opelco 4681 | . . . 4 |
11 | 7, 10 | mtbir 645 | . . 3 |
12 | noel 3337 | . . 3 | |
13 | 11, 12 | 2false 675 | . 2 |
14 | 1, 2, 13 | eqrelriiv 4603 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 wex 1453 wcel 1465 c0 3333 cop 3500 class class class wbr 3899 ccom 4513 |
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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-co 4518 |
This theorem is referenced by: co01 5023 |
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