ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.74ri Structured version   GIF version

Theorem pm5.74ri 170
Description: Distribution of implication over biconditional (reverse inference rule). (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
pm5.74ri.1 ((φψ) ↔ (φχ))
Assertion
Ref Expression
pm5.74ri (φ → (ψχ))

Proof of Theorem pm5.74ri
StepHypRef Expression
1 pm5.74ri.1 . 2 ((φψ) ↔ (φχ))
2 pm5.74 168 . 2 ((φ → (ψχ)) ↔ ((φψ) ↔ (φχ)))
31, 2mpbir 134 1 (φ → (ψχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bitrd  177  bibi2d  221  tbt  236  cbval2  1793  sbco2d  1837  sbco2vd  1838
  Copyright terms: Public domain W3C validator