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Theorem dff1o2 5726
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 5508 . 2
2 df-f1 5506 . . . 4
3 df-fo 5507 . . . 4
42, 3anbi12i 680 . . 3
5 anass 632 . . . 4
6 3anan12 950 . . . . . 6
76anbi1i 678 . . . . 5
8 eqimss 3389 . . . . . . . 8
9 df-f 5505 . . . . . . . . 9
109biimpri 199 . . . . . . . 8
118, 10sylan2 462 . . . . . . 7
12113adant2 977 . . . . . 6
1312pm4.71i 615 . . . . 5
14 ancom 439 . . . . 5
157, 13, 143bitr4ri 271 . . . 4
165, 15bitri 242 . . 3
174, 16bitri 242 . 2
181, 17bitri 242 1
Colors of variables: wff set class
Syntax hints:  <->wb 178  /\wa 360  /\w3a 937  =wceq 1654  C_wss 3309  `'ccnv 4918  rancrn 4920  Funwfun 5495  Fnwfn 5496  -->wf 5497  -1-1->wf1 5498  -onto->wfo 5499  -1-1-onto->wf1o 5500
This theorem is referenced by:  dff1o3  5727  dff1o4  5729  f1orn  5731  tz7.49c  6752  fiint  7432  dfrelog  20514  adj1o  23448  esumc  24495  stoweidlem39  27942
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-in 3316  df-ss 3323  df-f 5505  df-f1 5506  df-fo 5507  df-f1o 5508
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