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Mirrors > Home > NFE Home > Th. List > intprg | Unicode version |
Description: The intersection of a pair is the intersection of its members. Closed form of intpr 3959. Theorem 71 of [Suppes] p. 42. (Contributed by FL, 27-Apr-2008.) |
Ref | Expression |
---|---|
intprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3799 |
. . . 4
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2 | 1 | inteqd 3931 |
. . 3
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3 | ineq1 3450 |
. . 3
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4 | 2, 3 | eqeq12d 2367 |
. 2
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5 | preq2 3800 |
. . . 4
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6 | 5 | inteqd 3931 |
. . 3
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7 | ineq2 3451 |
. . 3
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8 | 6, 7 | eqeq12d 2367 |
. 2
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9 | vex 2862 |
. . 3
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10 | vex 2862 |
. . 3
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11 | 9, 10 | intpr 3959 |
. 2
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12 | 4, 8, 11 | vtocl2g 2918 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-sn 3741 df-pr 3742 df-int 3927 |
This theorem is referenced by: intsng 3961 |
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