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

Theorem cbvexd 1989
 Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim 2074. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
cbvald.1
cbvald.2
cbvald.3
Assertion
Ref Expression
cbvexd
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   ()

Proof of Theorem cbvexd
StepHypRef Expression
1 cbvald.1 . . . 4
2 cbvald.2 . . . . 5
32nfnd 1810 . . . 4
4 cbvald.3 . . . . 5
5 notbi 288 . . . . 5
64, 5syl6ib 219 . . . 4
71, 3, 6cbvald 1987 . . 3
87notbid 287 . 2
9 df-ex 1552 . 2
10 df-ex 1552 . 2
118, 9, 103bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178  wal 1550  wex 1551  wnf 1554 This theorem is referenced by:  cbvexdva  1996  vtoclgft  3004  dfid3  4502  axrepndlem2  8473  axunnd  8476  axpowndlem2  8478  axpownd  8481  axregndlem2  8483  axinfndlem1  8485  axacndlem4  8490 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
 Copyright terms: Public domain W3C validator