Theorem fdmrn 5751

Description: A different way to write is a function. (Contributed by Thierry Arnoux, 7-Dec-2016.)

Assertion

Ref	Expression
fdmrn

Proof of Theorem fdmrn

Step	Hyp	Ref	Expression
1		ssid 3522	. . 3
2		df-f 5597	. . 3
3	1, 2	mpbiran2 919	. 2
4		eqid 2457	. . 3
5		df-fn 5596	. . 3
6	4, 5	mpbiran2 919	. 2
7	3, 6	bitr2i 250	1

Syntax hints:  <->wb 184  =wceq 1395  C_wss 3475  domcdm 5004  rancrn 5005  Funwfun 5587  Fnwfn 5588  -->wf 5589

This theorem is referenced by:  nvof1o  6186  rinvf1o  27472  locfinref  27844  limccog  31626

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