NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  a1bi GIF version

Theorem a1bi 327
Description: Inference rule introducing a theorem as an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 11-Nov-2012.)
Hypothesis
Ref Expression
a1bi.1 φ
Assertion
Ref Expression
a1bi (ψ ↔ (φψ))

Proof of Theorem a1bi
StepHypRef Expression
1 a1bi.1 . 2 φ
2 biimt 325 . 2 (φ → (ψ ↔ (φψ)))
31, 2ax-mp 5 1 (ψ ↔ (φψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177
This theorem is referenced by:  mt2bi  328  pm4.83  895  truimfal  1345  equsalhw  1838  equveli  1988  sbequ8  2079  ralv  2873  ssopr  4847
  Copyright terms: Public domain W3C validator