Theorem iotajust 5555

Description: Soundness justification theorem for df-iota 5556. (Contributed by Andrew Salmon, 29-Jun-2011.)

Assertion

Ref	Expression
iotajust

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem iotajust

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		sneq 4039	. . . . 5
2	1	eqeq2d 2471	. . . 4
3	2	cbvabv 2600	. . 3
4		sneq 4039	. . . . 5
5	4	eqeq2d 2471	. . . 4
6	5	cbvabv 2600	. . 3
7	3, 6	eqtri 2486	. 2
8	7	unieqi 4258	1

Syntax hints:  =wceq 1395  {cab 2442  {csn 4029  U.cuni 4249

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