Users' Mathboxes Mathbox for Wolf Lammen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wl-syls1 Structured version   Visualization version   GIF version

Theorem wl-syls1 35323
Description: Replacing a nested consequent. A sort of syllogism in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
wl-syls1.1 (𝜓𝜒)
wl-syls1.2 ((𝜑𝜒) → 𝜃)
Assertion
Ref Expression
wl-syls1 ((𝜑𝜓) → 𝜃)

Proof of Theorem wl-syls1
StepHypRef Expression
1 wl-syls1.1 . . 3 (𝜓𝜒)
21a1i 11 . 2 (𝜑 → (𝜓𝜒))
3 wl-syls1.2 . 2 ((𝜑𝜒) → 𝜃)
42, 3wl-mps 35322 1 ((𝜑𝜓) → 𝜃)
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