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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ffnafv | Structured version Visualization version Unicode version |
Description: A function maps to a class to which all values belong, analogous to ffnfv 6032. (Contributed by Alexander van der Vekens, 25-May-2017.) |
Ref | Expression |
---|---|
ffnafv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 5710 |
. . 3
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2 | fafvelrn 38762 |
. . . 4
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3 | 2 | ralrimiva 2789 |
. . 3
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4 | 1, 3 | jca 539 |
. 2
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5 | simpl 463 |
. . 3
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6 | afvelrnb0 38756 |
. . . . 5
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7 | nfra1 2765 |
. . . . . 6
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8 | nfv 1764 |
. . . . . 6
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9 | rsp 2753 |
. . . . . . 7
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10 | eleq1 2517 |
. . . . . . . 8
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11 | 10 | biimpcd 232 |
. . . . . . 7
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12 | 9, 11 | syl6 34 |
. . . . . 6
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13 | 7, 8, 12 | rexlimd 2846 |
. . . . 5
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14 | 6, 13 | sylan9 667 |
. . . 4
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15 | 14 | ssrdv 3405 |
. . 3
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16 | df-f 5564 |
. . 3
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17 | 5, 15, 16 | sylanbrc 675 |
. 2
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18 | 4, 17 | impbii 192 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-9 1899 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 ax-sep 4496 ax-nul 4505 ax-pr 4611 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1450 df-ex 1667 df-nf 1671 df-sb 1801 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3014 df-sbc 3235 df-dif 3374 df-un 3376 df-in 3378 df-ss 3385 df-nul 3699 df-if 3849 df-sn 3936 df-pr 3938 df-op 3942 df-uni 4168 df-br 4374 df-opab 4433 df-mpt 4434 df-id 4726 df-xp 4817 df-rel 4818 df-cnv 4819 df-co 4820 df-dm 4821 df-rn 4822 df-res 4823 df-iota 5524 df-fun 5562 df-fn 5563 df-f 5564 df-fv 5568 df-dfat 38707 df-afv 38708 |
This theorem is referenced by: ffnaov 38791 |
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