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Mirrors > Home > ILE Home > Th. List > int0 | Unicode version |
Description: The intersection of the empty set is the universal class. Exercise 2 of [TakeutiZaring] p. 44. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
int0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3441 |
. . . . . 6
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2 | 1 | pm2.21i 647 |
. . . . 5
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3 | 2 | ax-gen 1460 |
. . . 4
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4 | equid 1712 |
. . . 4
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5 | 3, 4 | 2th 174 |
. . 3
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6 | 5 | abbii 2305 |
. 2
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7 | df-int 3860 |
. 2
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8 | df-v 2754 |
. 2
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9 | 6, 7, 8 | 3eqtr4i 2220 |
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-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-dif 3146 df-nul 3438 df-int 3860 |
This theorem is referenced by: rint0 3898 intexr 4168 fiintim 6957 elfi2 7001 fi0 7004 bj-intexr 15118 |
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