ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3adantl1 Unicode version

Theorem 3adantl1 1148
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
3adantl1  |-  ( ( ( ta  /\  ph  /\ 
ps )  /\  ch )  ->  th )

Proof of Theorem 3adantl1
StepHypRef Expression
1 3simpc 991 . 2  |-  ( ( ta  /\  ph  /\  ps )  ->  ( ph  /\ 
ps ) )
2 3adantl.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylan 281 1  |-  ( ( ( ta  /\  ph  /\ 
ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 973
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 975
This theorem is referenced by:  3ad2antl2  1155  3ad2antl3  1156  distrlem1prl  7531  distrlem1pru  7532  divmuldivap  8616  modqaddmulmod  10334  expnlbnd  10587  lcmledvds  12011  ctinf  12372  upxp  13025
  Copyright terms: Public domain W3C validator