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Mirrors > Home > MPE Home > Th. List > nfixp | Structured version Visualization version Unicode version |
Description: Bound-variable hypothesis builder for indexed Cartesian product. (Contributed by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfixp.1 |
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nfixp.2 |
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Ref | Expression |
---|---|
nfixp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ixp 7523 |
. 2
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2 | nfcv 2592 |
. . . . 5
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3 | nftru 1677 |
. . . . . . 7
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4 | nfcvf 2615 |
. . . . . . . . 9
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5 | 4 | adantl 468 |
. . . . . . . 8
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6 | nfixp.1 |
. . . . . . . . 9
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7 | 6 | a1i 11 |
. . . . . . . 8
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8 | 5, 7 | nfeld 2600 |
. . . . . . 7
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9 | 3, 8 | nfabd2 2611 |
. . . . . 6
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10 | 9 | trud 1453 |
. . . . 5
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11 | 2, 10 | nffn 5672 |
. . . 4
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12 | df-ral 2742 |
. . . . 5
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13 | 2 | a1i 11 |
. . . . . . . . . 10
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14 | 13, 5 | nffvd 5874 |
. . . . . . . . 9
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15 | nfixp.2 |
. . . . . . . . . 10
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16 | 15 | a1i 11 |
. . . . . . . . 9
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17 | 14, 16 | nfeld 2600 |
. . . . . . . 8
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18 | 8, 17 | nfimd 2000 |
. . . . . . 7
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19 | 3, 18 | nfald2 2165 |
. . . . . 6
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20 | 19 | trud 1453 |
. . . . 5
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21 | 12, 20 | nfxfr 1696 |
. . . 4
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22 | 11, 21 | nfan 2011 |
. . 3
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23 | 22 | nfab 2596 |
. 2
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24 | 1, 23 | nfcxfr 2590 |
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-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-iota 5546 df-fun 5584 df-fn 5585 df-fv 5590 df-ixp 7523 |
This theorem is referenced by: (None) |
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