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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1f 5328 | . . 3 | |
2 | fss 5284 | . . 3 | |
3 | 1, 2 | sylan 281 | . 2 |
4 | df-f1 5128 | . . . 4 | |
5 | 4 | simprbi 273 | . . 3 |
6 | 5 | adantr 274 | . 2 |
7 | df-f1 5128 | . 2 | |
8 | 3, 6, 7 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wss 3071 ccnv 4538 wfun 5117 wf 5119 wf1 5120 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-in 3077 df-ss 3084 df-f 5127 df-f1 5128 |
This theorem is referenced by: f1sng 5409 |
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