MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  cbv1 Unicode version

Theorem cbv1 2017
Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) Format hypotheses to common style. (Revised by Wolf Lammen, 13-May-2018.)
Hypotheses
Ref Expression
cbv1.1
cbv1.2
cbv1.3
cbv1.4
cbv1.5
Assertion
Ref Expression
cbv1

Proof of Theorem cbv1
StepHypRef Expression
1 cbv1.2 . . . . 5
2 cbv1.3 . . . . 5
31, 2nfim1 1919 . . . 4
4 cbv1.1 . . . . 5
5 cbv1.4 . . . . 5
64, 5nfim1 1919 . . . 4
7 cbv1.5 . . . . . 6
87com12 31 . . . . 5
98a2d 26 . . . 4
103, 6, 9cbv3 2015 . . 3
11419.21 1905 . . 3
12119.21 1905 . . 3
1310, 11, 123imtr3i 265 . 2
1413pm2.86i 101 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393  F/wnf 1616
This theorem is referenced by:  cbv1h  2018
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
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
  Copyright terms: Public domain W3C validator