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Theorem dff1o2 5679
 Description: Alternate definition of one-to-one onto function. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)
Assertion
Ref Expression
dff1o2

Proof of Theorem dff1o2
StepHypRef Expression
1 df-f1o 5461 . 2
2 df-f1 5459 . . . 4
3 df-fo 5460 . . . 4
42, 3anbi12i 679 . . 3
5 anass 631 . . . 4
6 3anan12 949 . . . . . 6
76anbi1i 677 . . . . 5
8 eqimss 3400 . . . . . . . 8
9 df-f 5458 . . . . . . . . 9
109biimpri 198 . . . . . . . 8
118, 10sylan2 461 . . . . . . 7
12113adant2 976 . . . . . 6
1312pm4.71i 614 . . . . 5
14 ancom 438 . . . . 5
157, 13, 143bitr4ri 270 . . . 4
165, 15bitri 241 . . 3
174, 16bitri 241 . 2
181, 17bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   w3a 936   wceq 1652   wss 3320  ccnv 4877   crn 4879   wfun 5448   wfn 5449  wf 5450  wf1 5451  wfo 5452  wf1o 5453 This theorem is referenced by:  dff1o3  5680  dff1o4  5682  f1orn  5684  tz7.49c  6703  fiint  7383  dfrelog  20463  adj1o  23397  esumc  24446  stoweidlem39  27764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-in 3327  df-ss 3334  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461
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