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Mirrors > Home > MPE Home > Th. List > iinin1 | Unicode version |
Description: Indexed intersection of intersection. Generalization of half of theorem "Distributive laws" in [Enderton] p. 30. Use intiin 4105 to recover Enderton's theorem. (Contributed by Mario Carneiro, 19-Mar-2015.) |
Ref | Expression |
---|---|
iinin1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iinin2 4121 |
. 2
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2 | incom 3493 |
. . . 4
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3 | 2 | a1i 11 |
. . 3
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4 | 3 | iineq2i 4072 |
. 2
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5 | incom 3493 |
. 2
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6 | 1, 4, 5 | 3eqtr4g 2461 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: firest 13615 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 |
This theorem depends on definitions: df-bi 178 df-an 361 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-v 2918 df-dif 3283 df-in 3287 df-nul 3589 df-iin 4056 |
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