Theorem dff1o5 5830

Description: Alternate definition of one-to-one onto function. (Contributed by NM, 10-Dec-2003.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)

Assertion

Ref	Expression
dff1o5

Proof of Theorem dff1o5

Step	Hyp	Ref	Expression
1		df-f1o 5600	. 2
2		f1f 5786	. . . . 5
3	2	biantrurd 508	. . . 4
4		dffo2 5804	. . . 4
5	3, 4	syl6rbbr 264	. . 3
6	5	pm5.32i 637	. 2
7	1, 6	bitri 249	1

Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  rancrn 5005  -->wf 5589  -1-1->wf1 5590  -onto->wfo 5591  -1-1-onto->wf1o 5592

This theorem is referenced by:  f1orescnv  5836  domdifsn  7620  sucdom2  7734  ackbij1  8639  ackbij2  8644  fin4en1  8710  om2uzf1oi  12064  s4f1o  12866  fvcosymgeq  16454  indlcim  18875  ausisusgra  24355  usgraexmpledg  24403  pwssplit4  31035  cdleme50f1o  36272  diaf1oN  36857

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-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