Theorem eqsbc3r 3389

Description: eqsbc3 3367 with setvar variable on right side of equals sign. This proof was automatically generated from the virtual deduction proof eqsbc3rVD 33640 using a translation program. (Contributed by Alan Sare, 24-Oct-2011.)

Assertion

Ref	Expression
eqsbc3r

Distinct variable groups:   ,   ,

Proof of Theorem eqsbc3r

Step	Hyp	Ref	Expression
1		eqcom 2466	. . . . . 6
2	1	sbcbii 3387	. . . . 5
3	2	biimpi 194	. . . 4
4		eqsbc3 3367	. . . 4
5	3, 4	syl5ib 219	. . 3
6		eqcom 2466	. . 3
7	5, 6	syl6ib 226	. 2
8		idd 24	. . . . 5
9	8, 6	syl6ibr 227	. . . 4
10	9, 4	sylibrd 234	. . 3
11	10, 2	syl6ibr 227	. 2
12	7, 11	impbid 191	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  [.wsbc 3327

This theorem is referenced by:  sbcoreleleq  33306  sbcoreleleqVD  33659

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-v 3111  df-sbc 3328