Theorem injust 3481

Description: Soundness justification theorem for df-in 3482. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

Ref	Expression
injust

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem injust

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		eleq1 2529	. . . 4
2		eleq1 2529	. . . 4
3	1, 2	anbi12d 710	. . 3
4	3	cbvabv 2600	. 2
5		eleq1 2529	. . . 4
6		eleq1 2529	. . . 4
7	5, 6	anbi12d 710	. . 3
8	7	cbvabv 2600	. 2
9	4, 8	eqtri 2486	1

Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442

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-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452