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Mirrors > Home > ILE Home > Th. List > fnsnfv | Unicode version |
Description: Singleton of function value. (Contributed by NM, 22-May-1998.) |
Ref | Expression |
---|---|
fnsnfv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2142 |
. . . 4
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2 | fnbrfvb 5470 |
. . . 4
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3 | 1, 2 | syl5bb 191 |
. . 3
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4 | 3 | abbidv 2258 |
. 2
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5 | df-sn 3538 |
. . 3
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6 | 5 | a1i 9 |
. 2
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7 | imasng 4912 |
. . 3
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8 | 7 | adantl 275 |
. 2
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9 | 4, 6, 8 | 3eqtr4d 2183 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-fv 5139 |
This theorem is referenced by: fnimapr 5489 funfvdm 5492 fvco2 5498 fvimacnvi 5542 fsn2 5602 phplem4 6757 phplem4dom 6764 phplem4on 6769 fiintim 6825 fidcenumlemrks 6849 fidcenumlemr 6851 resunimafz0 10606 ennnfonelemhf1o 11962 |
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