ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3ad2antl3 Unicode version

Theorem 3ad2antl3 1145
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
3ad2antl.1  |-  ( (
ph  /\  ch )  ->  th )
Assertion
Ref Expression
3ad2antl3  |-  ( ( ( ps  /\  ta  /\ 
ph )  /\  ch )  ->  th )

Proof of Theorem 3ad2antl3
StepHypRef Expression
1 3ad2antl.1 . . 3  |-  ( (
ph  /\  ch )  ->  th )
21adantll 467 . 2  |-  ( ( ( ta  /\  ph )  /\  ch )  ->  th )
323adantl1 1137 1  |-  ( ( ( ps  /\  ta  /\ 
ph )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  rspc3ev  2806  brcogw  4708  cocan1  5688  ov6g  5908  prarloclemarch2  7227  ltpopr  7403  ltsopr  7404  zdivmul  9141  lcmdvds  11760
  Copyright terms: Public domain W3C validator