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Theorem dff1o2 5826
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 5600 . 2
2 df-f1 5598 . . . 4
3 df-fo 5599 . . . 4
42, 3anbi12i 697 . . 3
5 anass 649 . . . 4
6 3anan12 986 . . . . . 6
76anbi1i 695 . . . . 5
8 eqimss 3555 . . . . . . . 8
9 df-f 5597 . . . . . . . . 9
109biimpri 206 . . . . . . . 8
118, 10sylan2 474 . . . . . . 7
12113adant2 1015 . . . . . 6
1312pm4.71i 632 . . . . 5
14 ancom 450 . . . . 5
157, 13, 143bitr4ri 278 . . . 4
165, 15bitri 249 . . 3
174, 16bitri 249 . 2
181, 17bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  C_wss 3475  `'ccnv 5003  rancrn 5005  Funwfun 5587  Fnwfn 5588  -->wf 5589  -1-1->wf1 5590  -onto->wfo 5591  -1-1-onto->wf1o 5592
This theorem is referenced by:  dff1o3  5827  dff1o4  5829  f1orn  5831  tz7.49c  7130  fiint  7817  symgfixelsi  16460  dfrelog  22953  adj1o  26813  esumc  28062  stoweidlem39  31821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-in 3482  df-ss 3489  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600
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