Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e11an Structured version   Visualization version   GIF version

Theorem e11an 39416
Description: Conjunction form of e11 39415. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e11an.1 (   𝜑   ▶   𝜓   )
e11an.2 (   𝜑   ▶   𝜒   )
e11an.3 ((𝜓𝜒) → 𝜃)
Assertion
Ref Expression
e11an (   𝜑   ▶   𝜃   )

Proof of Theorem e11an
StepHypRef Expression
1 e11an.1 . 2 (   𝜑   ▶   𝜓   )
2 e11an.2 . 2 (   𝜑   ▶   𝜒   )
3 e11an.3 . . 3 ((𝜓𝜒) → 𝜃)
43ex 449 . 2 (𝜓 → (𝜒𝜃))
51, 2, 4e11 39415 1 (   𝜑   ▶   𝜃   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  (   wvd1 39287
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 197  df-an 385  df-vd1 39288
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator