MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  jarr Structured version   Visualization version   GIF version

Theorem jarr 106
Description: Elimination of a nested antecedent as a partial converse of ja 173 (the other being jarl 175). (Contributed by Wolf Lammen, 9-May-2013.)
Assertion
Ref Expression
jarr (((𝜑𝜓) → 𝜒) → (𝜓𝜒))

Proof of Theorem jarr
StepHypRef Expression
1 ax-1 6 . 2 (𝜓 → (𝜑𝜓))
21imim1i 63 1 (((𝜑𝜓) → 𝜒) → (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  loolin  110  loowoz  111  minimp  1600  bj-jarri  32661  ax3h  41381
  Copyright terms: Public domain W3C validator