Theorem iotaint 5569

Description: Equivalence between two different forms of iota. (Contributed by Mario Carneiro, 24-Dec-2016.)

Assertion

Ref	Expression
iotaint

Proof of Theorem iotaint

Step	Hyp	Ref	Expression
1		iotauni 5568	. 2
2		uniintab 4325	. . 3
3	2	biimpi 194	. 2
4	1, 3	eqtrd 2498	1

Syntax hints:  ->wi 4  =wceq 1395  E!weu 2282  {cab 2442  U.cuni 4249  |^|cint 4286  iotacio 5554

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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032  df-uni 4250  df-int 4287  df-iota 5556