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Mirrors > Home > ILE Home > Th. List > f1ss | Unicode version |
Description: A function that is one-to-one is also one-to-one on some superset of its range. (Contributed by Mario Carneiro, 12-Jan-2013.) |
Ref | Expression |
---|---|
f1ss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1f 5251 |
. . 3
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2 | fss 5207 |
. . 3
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3 | 1, 2 | sylan 278 |
. 2
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4 | df-f1 5054 |
. . . 4
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5 | 4 | simprbi 270 |
. . 3
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6 | 5 | adantr 271 |
. 2
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7 | df-f1 5054 |
. 2
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8 | 3, 6, 7 | sylanbrc 409 |
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 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-11 1449 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-in 3019 df-ss 3026 df-f 5053 df-f1 5054 |
This theorem is referenced by: (None) |
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