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Mirrors > Home > ILE Home > Th. List > f1ocnv | Unicode version |
Description: The converse of a one-to-one onto function is also one-to-one onto. (Contributed by NM, 11-Feb-1997.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
f1ocnv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnrel 5315 |
. . . . 5
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2 | dfrel2 5080 |
. . . . . 6
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3 | fneq1 5305 |
. . . . . . 7
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4 | 3 | biimprd 158 |
. . . . . 6
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5 | 2, 4 | sylbi 121 |
. . . . 5
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6 | 1, 5 | mpcom 36 |
. . . 4
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7 | 6 | anim2i 342 |
. . 3
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8 | 7 | ancoms 268 |
. 2
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9 | dff1o4 5470 |
. 2
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10 | dff1o4 5470 |
. 2
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11 | 8, 9, 10 | 3imtr4i 201 |
1
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