Theorem sb8iota 5563

Description: Variable substitution in description binder. Compare sb8eu 2318. (Contributed by NM, 18-Mar-2013.)

Hypothesis

Ref	Expression
sb8iota.1

Assertion

Ref	Expression
sb8iota

Proof of Theorem sb8iota

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		nfv 1707	. . . . . 6
2	1	sb8 2167	. . . . 5
3		sbbi 2142	. . . . . . 7
4		sb8iota.1	. . . . . . . . 9
5	4	nfsb 2184	. . . . . . . 8
6		equsb3 2176	. . . . . . . . 9
7		nfv 1707	. . . . . . . . 9
8	6, 7	nfxfr 1645	. . . . . . . 8
9	5, 8	nfbi 1934	. . . . . . 7
10	3, 9	nfxfr 1645	. . . . . 6
11		nfv 1707	. . . . . 6
12		sbequ 2117	. . . . . 6
13	10, 11, 12	cbval 2021	. . . . 5
14		equsb3 2176	. . . . . . 7
15	14	sblbis 2145	. . . . . 6
16	15	albii 1640	. . . . 5
17	2, 13, 16	3bitri 271	. . . 4
18	17	abbii 2591	. . 3
19	18	unieqi 4258	. 2
20		dfiota2 5557	. 2
21		dfiota2 5557	. 2
22	19, 20, 21	3eqtr4i 2496	1

Syntax hints:  <->wb 184  A.wal 1393  =wceq 1395  F/wnf 1616  [wsb 1739  {cab 2442  U.cuni 4249  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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-sn 4030  df-uni 4250  df-iota 5556