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Theorem f1funfun 5263
 Description: Two ways to express that a set is one-to-one. Each side is equivalent to Definition 6.4(3) of [TakeutiZaring] p. 24, who use the notation "Un2 (A)" for one-to-one. We do not introduce a separate notation since we rarely use it. (Contributed by set.mm contributors, 13-Aug-2004.) (Revised by Scott Fenton, 18-Apr-2021.)
Assertion
Ref Expression
f1funfun

Proof of Theorem f1funfun
StepHypRef Expression
1 df-f1 4792 . 2
2 ancom 437 . 2
3 ssv 3291 . . . . 5
4 df-f 4791 . . . . 5
53, 4mpbiran2 885 . . . 4
6 funfn 5136 . . . 4
75, 6bitr4i 243 . . 3
87anbi2i 675 . 2
91, 2, 83bitri 262 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  cvv 2859   wss 3257  ccnv 4771   cdm 4772   crn 4773   wfun 4775   wfn 4776  wf 4777  wf1 4778 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-fn 4790  df-f 4791  df-f1 4792 This theorem is referenced by: (None)
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