Theorem iotassuni 5572

Description: The iota class is a subset of the union of all elements satisfying . (Contributed by Mario Carneiro, 24-Dec-2016.)

Assertion

Ref	Expression
iotassuni

Proof of Theorem iotassuni

Step	Hyp	Ref	Expression
1		iotauni 5568	. . 3
2		eqimss 3555	. . 3
3	1, 2	syl 16	. 2
4		iotanul 5571	. . 3
5		0ss 3814	. . 3
6	4, 5	syl6eqss 3553	. 2
7	3, 6	pm2.61i 164	1

Syntax hints:  -.wn 3  =wceq 1395  E!weu 2282  {cab 2442  C_wss 3475  c0 3784  U.cuni 4249  iotacio 5554

This theorem is referenced by:  bj-nuliotaALT  34587

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-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-iota 5556