Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eel0321old Structured version   Visualization version   GIF version

Theorem eel0321old 37962
 Description: el0321old 37963 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel0321old.1 𝜑
eel0321old.2 ((𝜓𝜒𝜃) → 𝜏)
eel0321old.3 ((𝜑𝜏) → 𝜂)
Assertion
Ref Expression
eel0321old ((𝜓𝜒𝜃) → 𝜂)

Proof of Theorem eel0321old
StepHypRef Expression
1 eel0321old.1 . 2 𝜑
2 eel0321old.2 . 2 ((𝜓𝜒𝜃) → 𝜏)
3 eel0321old.3 . 2 ((𝜑𝜏) → 𝜂)
41, 2, 3sylancr 694 1 ((𝜓𝜒𝜃) → 𝜂)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031 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 196  df-an 385 This theorem is referenced by:  el0321old  37963  suctrALTcf  38180
 Copyright terms: Public domain W3C validator