Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eelT0 Structured version   Visualization version   GIF version

Theorem eelT0 38470
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eelT0.1 (⊤ → 𝜑)
eelT0.2 𝜓
eelT0.3 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
eelT0 𝜒

Proof of Theorem eelT0
StepHypRef Expression
1 eelT0.2 . . 3 𝜓
2 eelT0.1 . . . 4 (⊤ → 𝜑)
3 eelT0.3 . . . 4 ((𝜑𝜓) → 𝜒)
42, 3sylan 488 . . 3 ((⊤ ∧ 𝜓) → 𝜒)
51, 4mpan2 706 . 2 (⊤ → 𝜒)
65trud 1490 1 𝜒
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wtru 1481
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 386  df-tru 1483
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator