ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  cbvaldva Structured version   GIF version

Theorem cbvaldva 1800
Description: Rule used to change the bound variable in a universal quantifier with implicit substitution. Deduction form. (Contributed by David Moews, 1-May-2017.)
Hypothesis
Ref Expression
cbvaldva.1 ((φ x = y) → (ψχ))
Assertion
Ref Expression
cbvaldva (φ → (xψyχ))
Distinct variable groups:   ψ,y   χ,x   φ,x   φ,y
Allowed substitution hints:   ψ(x)   χ(y)

Proof of Theorem cbvaldva
StepHypRef Expression
1 nfv 1418 . 2 yφ
2 nfvd 1419 . 2 (φ → Ⅎyψ)
3 cbvaldva.1 . . 3 ((φ x = y) → (ψχ))
43ex 108 . 2 (φ → (x = y → (ψχ)))
51, 2, 4cbvald 1797 1 (φ → (xψyχ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  cbvraldva2  2531
  Copyright terms: Public domain W3C validator