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Mirrors > Home > ILE Home > Th. List > fnunsn | Unicode version |
Description: Extension of a function with a new ordered pair. (Contributed by NM, 28-Sep-2013.) (Revised by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
fnunop.x |
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fnunop.y |
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fnunop.f |
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fnunop.g |
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fnunop.e |
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fnunop.d |
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Ref | Expression |
---|---|
fnunsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnunop.f |
. . 3
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2 | fnunop.x |
. . . 4
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3 | fnunop.y |
. . . 4
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4 | fnsng 5301 |
. . . 4
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5 | 2, 3, 4 | syl2anc 411 |
. . 3
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6 | fnunop.d |
. . . 4
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7 | disjsn 3680 |
. . . 4
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8 | 6, 7 | sylibr 134 |
. . 3
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9 | fnun 5360 |
. . 3
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10 | 1, 5, 8, 9 | syl21anc 1248 |
. 2
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11 | fnunop.g |
. . . 4
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12 | 11 | fneq1i 5348 |
. . 3
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13 | fnunop.e |
. . . 4
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14 | 13 | fneq2i 5349 |
. . 3
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15 | 12, 14 | bitri 184 |
. 2
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16 | 10, 15 | sylibr 134 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2167 ax-ext 2175 ax-sep 4147 ax-pow 4203 ax-pr 4238 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2045 df-mo 2046 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-v 2762 df-dif 3155 df-un 3157 df-in 3159 df-ss 3166 df-nul 3447 df-pw 3603 df-sn 3624 df-pr 3625 df-op 3627 df-br 4030 df-opab 4091 df-id 4324 df-xp 4665 df-rel 4666 df-cnv 4667 df-co 4668 df-dm 4669 df-fun 5256 df-fn 5257 |
This theorem is referenced by: tfrlemisucfn 6377 tfr1onlemsucfn 6393 |
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