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Mirrors > Home > ILE Home > Th. List > dff1o4 | Unicode version |
Description: Alternate definition of one-to-one onto function. (Contributed by NM, 25-Mar-1998.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
dff1o4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dff1o2 5465 |
. 2
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2 | 3anass 982 |
. 2
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3 | df-rn 4636 |
. . . . . 6
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4 | 3 | eqeq1i 2185 |
. . . . 5
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5 | 4 | anbi2i 457 |
. . . 4
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6 | df-fn 5218 |
. . . 4
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7 | 5, 6 | bitr4i 187 |
. . 3
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8 | 7 | anbi2i 457 |
. 2
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9 | 1, 2, 8 | 3bitri 206 |
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-rn 4636 df-fn 5218 df-f 5219 df-f1 5220 df-fo 5221 df-f1o 5222 |
This theorem is referenced by: f1ocnv 5473 f1oun 5480 f1o00 5495 f1oi 5498 f1osn 5500 f1ompt 5666 f1ofveu 5860 f1ocnvd 6070 f1od2 6233 mapsnf1o2 6693 sbthlemi9 6961 mhmf1o 12793 grpinvf1o 12872 hmeof1o2 13679 |
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