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Mirrors > Home > MPE Home > Th. List > fsnunf | Structured version Visualization version Unicode version |
Description: Adjoining a point to a function gives a function. (Contributed by Stefan O'Rear, 28-Feb-2015.) |
Ref | Expression |
---|---|
fsnunf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 1008 |
. . 3
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2 | simp2l 1034 |
. . . . 5
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3 | simp3 1010 |
. . . . 5
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4 | f1osng 5853 |
. . . . 5
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5 | 2, 3, 4 | syl2anc 667 |
. . . 4
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6 | f1of 5814 |
. . . 4
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7 | 5, 6 | syl 17 |
. . 3
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8 | simp2r 1035 |
. . . 4
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9 | disjsn 4032 |
. . . 4
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10 | 8, 9 | sylibr 216 |
. . 3
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11 | fun 5746 |
. . 3
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12 | 1, 7, 10, 11 | syl21anc 1267 |
. 2
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13 | snssi 4116 |
. . . . 5
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14 | 13 | 3ad2ant3 1031 |
. . . 4
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15 | ssequn2 3607 |
. . . 4
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16 | 14, 15 | sylib 200 |
. . 3
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17 | 16 | feq3d 5716 |
. 2
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18 | 12, 17 | mpbid 214 |
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-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
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-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 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-br 4403 df-opab 4462 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 |
This theorem is referenced by: fsnunf2 6103 fnchoice 37350 nnsum4primeseven 38895 nnsum4primesevenALTV 38896 |
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