Theorem sbc3ie 3405

Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Mario Carneiro, 19-Jun-2014.) (Revised by Mario Carneiro, 29-Dec-2014.)

Hypotheses

Ref	Expression
sbc3ie.1
sbc3ie.2
sbc3ie.3
sbc3ie.4

Assertion

Ref	Expression
sbc3ie

Distinct variable groups:   ,,,   ,,   ,   ,,,

Proof of Theorem sbc3ie

Step	Hyp	Ref	Expression
1		sbc3ie.1	. 2
2		sbc3ie.2	. 2
3		sbc3ie.3	. . . 4
4	3	a1i 11	. . 3
5		sbc3ie.4	. . . 4
6	5	3expa 1196	. . 3
7	4, 6	sbcied 3364	. 2
8	1, 2, 7	sbc2ie 3403	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818  cvv 3109  [.wsbc 3327

This theorem is referenced by:  isdlat  15823  islmod  17516  isslmd  27745  rmydioph  30956  hdmap1fval  37524  hdmapfval  37557  hgmapfval  37616

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-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  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