Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbc3ie Unicode version

Theorem sbc3ie 2952
 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:   ,,,   ,,   ,   ,,,
Allowed substitution hints:   (,,)   ()   (,)

Proof of Theorem sbc3ie
StepHypRef Expression
1 sbc3ie.1 . 2
2 sbc3ie.2 . 2
3 sbc3ie.3 . . . 4
43a1i 9 . . 3
5 sbc3ie.4 . . . 4
653expa 1164 . . 3
74, 6sbcied 2915 . 2
81, 2, 7sbc2ie 2950 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   w3a 945   wceq 1314   wcel 1463  cvv 2658  wsbc 2880 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-sbc 2881 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator