Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  cbvex2 Unicode version

Theorem cbvex2 1894
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
cbval2.1
cbval2.2
cbval2.3
cbval2.4
cbval2.5
Assertion
Ref Expression
cbvex2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbvex2
StepHypRef Expression
1 cbval2.1 . . 3
21nfex 1616 . 2
3 cbval2.3 . . 3
43nfex 1616 . 2
5 nfv 1508 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfan 1544 . . . . 5
8 nfv 1508 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfan 1544 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 115 . . . . . 6
1312pm5.32d 445 . . . . 5
147, 10, 13cbvex 1729 . . . 4
15 19.42v 1878 . . . 4
16 19.42v 1878 . . . 4
1714, 15, 163bitr3i 209 . . 3
18 pm5.32 448 . . 3
1917, 18mpbir 145 . 2
202, 4, 19cbvex 1729 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wnf 1436  wex 1468 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-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1437 This theorem is referenced by:  cbvex2v  1896  cbvopab  3999  cbvoprab12  5845
 Copyright terms: Public domain W3C validator