New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  cbvabv GIF version

Theorem cbvabv 2472
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 26-May-1999.)
Hypothesis
Ref Expression
cbvabv.1 (x = y → (φψ))
Assertion
Ref Expression
cbvabv {x φ} = {y ψ}
Distinct variable groups:   φ,y   ψ,x
Allowed substitution hints:   φ(x)   ψ(y)

Proof of Theorem cbvabv
StepHypRef Expression
1 nfv 1619 . 2 yφ
2 nfv 1619 . 2 xψ
3 cbvabv.1 . 2 (x = y → (φψ))
41, 2, 3cbvab 2471 1 {x φ} = {y ψ}
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642  {cab 2339 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346 This theorem is referenced by:  ninjust  3210  uniiunlem  3353  dfif3  3672  pwjust  3723  snjust  3740  intab  3956  iotajust  4338
 Copyright terms: Public domain W3C validator