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Mirrors > Home > MPE Home > Th. List > dffun6f | Structured version Visualization version Unicode version |
Description: Definition of function, using bound-variable hypotheses instead of distinct variable conditions. (Contributed by NM, 9-Mar-1995.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
dffun6f.1 |
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dffun6f.2 |
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Ref | Expression |
---|---|
dffun6f |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dffun3 5611 |
. 2
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2 | nfcv 2602 |
. . . . . . 7
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3 | dffun6f.2 |
. . . . . . 7
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4 | nfcv 2602 |
. . . . . . 7
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5 | 2, 3, 4 | nfbr 4460 |
. . . . . 6
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6 | nfv 1771 |
. . . . . 6
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7 | breq2 4419 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 5, 6, 7 | cbvmo 2345 |
. . . . 5
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9 | 8 | albii 1701 |
. . . 4
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10 | mo2v 2316 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 10 | albii 1701 |
. . . 4
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12 | nfcv 2602 |
. . . . . . 7
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13 | dffun6f.1 |
. . . . . . 7
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14 | nfcv 2602 |
. . . . . . 7
![]() ![]() ![]() ![]() | |
15 | 12, 13, 14 | nfbr 4460 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() |
16 | 15 | nfmo 2326 |
. . . . 5
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17 | nfv 1771 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | breq1 4418 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | mobidv 2330 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 16, 17, 19 | cbval 2124 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 9, 11, 20 | 3bitr3ri 284 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21 | anbi2i 705 |
. 2
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23 | 1, 22 | bitr4i 260 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pr 4652 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rab 2757 df-v 3058 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-br 4416 df-opab 4475 df-id 4767 df-cnv 4860 df-co 4861 df-fun 5602 |
This theorem is referenced by: dffun6 5615 funopab 5633 funcnvmptOLD 28318 funcnvmpt 28319 |
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