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Mirrors > Home > ILE Home > Th. List > f1orn | Unicode version |
Description: A one-to-one function maps onto its range. (Contributed by NM, 13-Aug-2004.) |
Ref | Expression |
---|---|
f1orn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dff1o2 5465 |
. 2
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2 | eqid 2177 |
. . 3
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3 | df-3an 980 |
. . 3
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4 | 2, 3 | mpbiran2 941 |
. 2
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5 | 1, 4 | bitri 184 |
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-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3135 df-ss 3142 df-f 5219 df-f1 5220 df-fo 5221 df-f1o 5222 |
This theorem is referenced by: f1f1orn 5471 |
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