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

Theorem cbvexd 2026
 Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim 2079. (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:   ,   ,

Proof of Theorem cbvexd
StepHypRef Expression
1 cbvald.1 . . . 4
2 cbvald.2 . . . . 5
32nfnd 1902 . . . 4
4 cbvald.3 . . . . 5
5 notbi 295 . . . . 5
64, 5syl6ib 226 . . . 4
71, 3, 6cbvald 2025 . . 3
87notbid 294 . 2
9 df-ex 1613 . 2
10 df-ex 1613 . 2
118, 9, 103bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616 This theorem is referenced by:  cbvexdva  2033  vtoclgft  3157  dfid3  4801  axrepndlem2  8989  axunnd  8992  axpowndlem2  8994  axpowndlem2OLD  8995  axpownd  8999  axregndlem2  9001  axinfndlem1  9004  axacndlem4  9009  wl-mo2dnae  30019  wl-mo2t  30020 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