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Mirrors > Home > ILE Home > Th. List > funsn | Unicode version |
Description: A singleton of an ordered pair is a function. Theorem 10.5 of [Quine] p. 65. (Contributed by NM, 12-Aug-1994.) |
Ref | Expression |
---|---|
funsn.1 | |
funsn.2 |
Ref | Expression |
---|---|
funsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funsn.1 | . 2 | |
2 | funsn.2 | . 2 | |
3 | funsng 5228 | . 2 | |
4 | 1, 2, 3 | mp2an 423 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2135 cvv 2721 csn 3570 cop 3573 wfun 5176 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-fun 5184 |
This theorem is referenced by: funtp 5235 fun0 5240 fvsn 5674 |
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