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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relco 5148 |
. 2
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2 | rel0 4772 |
. 2
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3 | noel 3441 |
. . . . . . 7
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4 | df-br 4022 |
. . . . . . 7
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5 | 3, 4 | mtbir 672 |
. . . . . 6
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6 | 5 | intnanr 931 |
. . . . 5
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7 | 6 | nex 1511 |
. . . 4
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8 | vex 2755 |
. . . . 5
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9 | vex 2755 |
. . . . 5
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10 | 8, 9 | opelco 4820 |
. . . 4
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11 | 7, 10 | mtbir 672 |
. . 3
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12 | noel 3441 |
. . 3
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13 | 11, 12 | 2false 702 |
. 2
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14 | 1, 2, 13 | eqrelriiv 4741 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-br 4022 df-opab 4083 df-xp 4653 df-rel 4654 df-co 4656 |
This theorem is referenced by: co01 5164 |
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