Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.41vvvv GIF version

Theorem 19.41vvvv 1782
 Description: Theorem 19.41 of [Margaris] p. 90 with 4 quantifiers. (Contributed by FL, 14-Jul-2007.)
Assertion
Ref Expression
19.41vvvv (wxyz(φ ψ) ↔ (wxyzφ ψ))
Distinct variable groups:   ψ,w   ψ,x   ψ,y   ψ,z
Allowed substitution hints:   φ(x,y,z,w)

Proof of Theorem 19.41vvvv
StepHypRef Expression
1 19.41vvv 1781 . . 3 (xyz(φ ψ) ↔ (xyzφ ψ))
21exbii 1493 . 2 (wxyz(φ ψ) ↔ w(xyzφ ψ))
3 19.41v 1779 . 2 (w(xyzφ ψ) ↔ (wxyzφ ψ))
42, 3bitri 173 1 (wxyz(φ ψ) ↔ (wxyzφ ψ))
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ↔ wb 98  ∃wex 1378 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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424 This theorem depends on definitions:  df-bi 110 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator