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Mathbox for Richard Penner |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > fipjust | Structured version Visualization version Unicode version |
Description: A definition of the finite intersection property of a class based on closure under pair-wise intersection of its elements is independent of the dummy variables. (Contributed by Richard Penner, 1-Jan-2020.) |
Ref | Expression |
---|---|
fipjust |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ineq1 3629 |
. . 3
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2 | 1 | eleq1d 2515 |
. 2
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3 | ineq2 3630 |
. . 3
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4 | 3 | eleq1d 2515 |
. 2
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5 | 2, 4 | cbvral2v 3029 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ral 2744 df-v 3049 df-in 3413 |
This theorem is referenced by: (None) |
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