Users' Mathboxes Mathbox for Wolf Lammen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-jarri Structured version   Visualization version   GIF version

Theorem wl-jarri 32356
Description: Dropping a nested antecedent. This theorem is one of two reversions of ja 171. Since ja 171 is reversible, a nested (chain of) implication(s) is just a packed notation of two or more theorems/hypotheses with a common consequent. axc5c7 33104 is an instance of this idea. (Contributed by Wolf Lammen, 20-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Ref Expression
wl-jarri.1 ((𝜑𝜓) → 𝜒)
Ref Expression
wl-jarri (𝜓𝜒)

Proof of Theorem wl-jarri
StepHypRef Expression
1 ax-1 6 . 2 (𝜓 → (𝜑𝜓))
2 wl-jarri.1 . 2 ((𝜑𝜓) → 𝜒)
31, 2syl 17 1 (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: (None)
  Copyright terms: Public domain W3C validator