Theorem tz6.12-1 5887

Description: Function value. Theorem 6.12(1) of [TakeutiZaring] p. 27. (Contributed by NM, 30-Apr-2004.)

Assertion

Ref	Expression
tz6.12-1

Distinct variable groups:   ,   ,

Proof of Theorem tz6.12-1

Step	Hyp	Ref	Expression
1		df-fv 5601	. 2
2		iota1 5570	. . 3
3	2	biimpac 486	. 2
4	1, 3	syl5eq 2510	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  E!weu 2282   class class class wbr 4452  iotacio 5554  `cfv 5593

This theorem is referenced by:  tz6.12  5888  tz6.12c  5890  funbrfv  5911

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-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-fv 5601