Theorem fodmrnu 5808

Description: An onto function has unique domain and range. (Contributed by NM, 5-Nov-2006.)

Assertion

Ref	Expression
fodmrnu

Proof of Theorem fodmrnu

Step	Hyp	Ref	Expression
1		fofn 5802	. . 3
2		fofn 5802	. . 3
3		fndmu 5687	. . 3
4	1, 2, 3	syl2an 477	. 2
5		forn 5803	. . 3
6		forn 5803	. . 3
7	5, 6	sylan9req 2519	. 2
8	4, 7	jca 532	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  rancrn 5005  Fnwfn 5588  -onto->wfo 5591

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-fn 5596  df-f 5597  df-fo 5599