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Mirrors > Home > MPE Home > Th. List > nfdisj | Structured version Visualization version Unicode version |
Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
nfdisj.1 |
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nfdisj.2 |
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Ref | Expression |
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nfdisj |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdisj2 4375 |
. 2
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2 | nftru 1677 |
. . . . 5
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3 | nfcvf 2615 |
. . . . . . . 8
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4 | nfdisj.1 |
. . . . . . . . 9
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5 | 4 | a1i 11 |
. . . . . . . 8
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6 | 3, 5 | nfeld 2600 |
. . . . . . 7
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7 | nfdisj.2 |
. . . . . . . . 9
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8 | 7 | nfcri 2586 |
. . . . . . . 8
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9 | 8 | a1i 11 |
. . . . . . 7
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10 | 6, 9 | nfand 2008 |
. . . . . 6
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11 | 10 | adantl 468 |
. . . . 5
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12 | 2, 11 | nfmod2 2312 |
. . . 4
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13 | 12 | trud 1453 |
. . 3
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14 | 13 | nfal 2030 |
. 2
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15 | 1, 14 | nfxfr 1696 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-cleq 2444 df-clel 2447 df-nfc 2581 df-rmo 2745 df-disj 4374 |
This theorem is referenced by: disjxiun 4399 |
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