MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbc2iegf Unicode version

Theorem sbc2iegf 3402
Description: Conversion of implicit substitution to explicit class substitution. (Contributed by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
sbc2iegf.1
sbc2iegf.2
sbc2iegf.3
sbc2iegf.4
Assertion
Ref Expression
sbc2iegf
Distinct variable groups:   , ,   ,   ,   ,

Proof of Theorem sbc2iegf
StepHypRef Expression
1 simpl 457 . 2
2 simpl 457 . . . 4
3 sbc2iegf.4 . . . . 5
43adantll 713 . . . 4
5 nfv 1707 . . . 4
6 sbc2iegf.2 . . . . 5
76a1i 11 . . . 4
82, 4, 5, 7sbciedf 3363 . . 3
98adantll 713 . 2
10 nfv 1707 . . 3
11 sbc2iegf.3 . . 3
1210, 11nfan 1928 . 2
13 sbc2iegf.1 . . 3
1413a1i 11 . 2
151, 9, 12, 14sbciedf 3363 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  [.wsbc 3327
This theorem is referenced by:  sbc2ie  3403  opelopabaf  4776  elmptrab  20328
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
  Copyright terms: Public domain W3C validator