Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  eel011 Structured version   Unicode version

Theorem eel011 31744
Description: mp3an 1315 with antecedents in standard conjunction form and with two hypotheses which are implications. (Contributed by Alan Sare, 28-Aug-2016.)
Hypotheses
Ref Expression
eel011.1  |-  ph
eel011.2  |-  ( ps 
->  ch )
eel011.3  |-  ( ps 
->  th )
eel011.4  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
Assertion
Ref Expression
eel011  |-  ( ps 
->  ta )

Proof of Theorem eel011
StepHypRef Expression
1 eel011.2 . 2  |-  ( ps 
->  ch )
2 eel011.3 . 2  |-  ( ps 
->  th )
3 eel011.1 . . 3  |-  ph
4 eel011.4 . . 3  |-  ( (
ph  /\  ch  /\  th )  ->  ta )
53, 4mp3an1 1302 . 2  |-  ( ( ch  /\  th )  ->  ta )
61, 2, 5syl2anc 661 1  |-  ( ps 
->  ta )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 965
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 185  df-an 371  df-3an 967
This theorem is referenced by:  sineq0ALT  31986
  Copyright terms: Public domain W3C validator