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

Theorem albiim 1357
Description: Split a biconditional and distribute quantifier. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
albiim (x(φψ) ↔ (x(φψ) x(ψφ)))

Proof of Theorem albiim
StepHypRef Expression
1 dfbi2 368 . . 3 ((φψ) ↔ ((φψ) (ψφ)))
21albii 1339 . 2 (x(φψ) ↔ x((φψ) (ψφ)))
3 19.26 1350 . 2 (x((φψ) (ψφ)) ↔ (x(φψ) x(ψφ)))
42, 3bitri 173 1 (x(φψ) ↔ (x(φψ) x(ψφ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98  wal 1226
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 1316  ax-gen 1318
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  2albiim  1358  hbbid  1449  equveli  1624  spsbbi  1707  eu1  1907  eqss  2937  ssext  3931
  Copyright terms: Public domain W3C validator