Theorem riota1 6276

Description: Property of restricted iota. Compare iota1 5570. (Contributed by Mario Carneiro, 15-Oct-2016.)

Assertion

Ref	Expression
riota1

Distinct variable group:   ,

Proof of Theorem riota1

Step	Hyp	Ref	Expression
1		df-reu 2814	. . 3
2		iota1 5570	. . 3
3	1, 2	sylbi 195	. 2
4		df-riota 6257	. . 3
5	4	eqeq1i 2464	. 2
6	3, 5	syl6bbr 263	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E!weu 2282  E!wreu 2809  iotacio 5554  iota_crio 6256

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-reu 2814  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257