Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eel000cT Unicode version

Theorem eel000cT 28783
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel000cT.1  |-  ph
eel000cT.2  |-  ps
eel000cT.3  |-  ch
eel000cT.4  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
eel000cT  |-  (  T. 
->  th )

Proof of Theorem eel000cT
StepHypRef Expression
1 eel000cT.3 . . 3  |-  ch
2 eel000cT.2 . . . 4  |-  ps
3 eel000cT.1 . . . . 5  |-  ph
4 eel000cT.4 . . . . 5  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
53, 4mp3an1 1264 . . . 4  |-  ( ( ps  /\  ch )  ->  th )
62, 5mpan 651 . . 3  |-  ( ch 
->  th )
71, 6ax-mp 8 . 2  |-  th
87a1i 10 1  |-  (  T. 
->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934    T. wtru 1307
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
  Copyright terms: Public domain W3C validator