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Mirrors > Home > ILE Home > Th. List > dff1o5 | Unicode version |
Description: Alternate definition of one-to-one onto function. (Contributed by NM, 10-Dec-2003.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
dff1o5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o 5037 |
. 2
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2 | f1f 5231 |
. . . . 5
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3 | 2 | biantrurd 300 |
. . . 4
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4 | dffo2 5252 |
. . . 4
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5 | 3, 4 | syl6rbbr 198 |
. . 3
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6 | 5 | pm5.32i 443 |
. 2
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7 | 1, 6 | bitri 183 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-in 3008 df-ss 3015 df-f 5034 df-f1 5035 df-fo 5036 df-f1o 5037 |
This theorem is referenced by: f1orescnv 5284 f1finf1o 6712 djuinr 6811 frec2uzf1od 9876 |
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