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Theorem f1ss 5334
 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

Proof of Theorem f1ss
StepHypRef Expression
1 f1f 5328 . . 3
2 fss 5284 . . 3
31, 2sylan 281 . 2
4 df-f1 5128 . . . 4
54simprbi 273 . . 3
7 df-f1 5128 . 2
83, 6, 7sylanbrc 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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