Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ad5ant1345 Unicode version

Theorem ad5ant1345 28543
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant1345.1  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
ad5ant1345  |-  ( ( ( ( ( ph  /\  et )  /\  ps )  /\  ch )  /\  th )  ->  ta )

Proof of Theorem ad5ant1345
StepHypRef Expression
1 ad5ant1345.1 . . . . 5  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
21exp41 593 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
32a1d 22 . . 3  |-  ( ph  ->  ( et  ->  ( ps  ->  ( ch  ->  ( th  ->  ta )
) ) ) )
43imp 418 . 2  |-  ( (
ph  /\  et )  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
54imp41 576 1  |-  ( ( ( ( ( ph  /\  et )  /\  ps )  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
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
  Copyright terms: Public domain W3C validator