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Theorem f1ss 5040
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.)
Assertion
Ref Expression
f1ss  F : -1-1->  C_  C  F : -1-1-> C

Proof of Theorem f1ss
StepHypRef Expression
1 f1f 5035 . . 3  F : -1-1->  F : -->
2 fss 4997 . . 3  F : -->  C_  C 
F : --> C
31, 2sylan 267 . 2  F : -1-1->  C_  C  F : --> C
4 df-f1 4850 . . . 4  F : -1-1->  F : -->  Fun  `' F
54simprbi 260 . . 3  F : -1-1->  Fun  `' F
65adantr 261 . 2  F : -1-1->  C_  C  Fun  `' F
7 df-f1 4850 . 2  F : -1-1-> C  F : --> C  Fun  `' F
83, 6, 7sylanbrc 394 1  F : -1-1->  C_  C  F : -1-1-> C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97    C_ wss 2911   `'ccnv 4287   Fun wfun 4839   -->wf 4841   -1-1->wf1 4842
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925  df-f 4849  df-f1 4850
This theorem is referenced by: (None)
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