ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ad6antr Unicode version

Theorem ad6antr 490
Description: Deduction adding 6 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypothesis
Ref Expression
ad2ant.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
ad6antr  |-  ( ( ( ( ( ( ( ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  ->  ps )

Proof of Theorem ad6antr
StepHypRef Expression
1 ad2ant.1 . . 3  |-  ( ph  ->  ps )
21ad5antr 488 . 2  |-  ( ( ( ( ( (
ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  ->  ps )
32adantr 274 1  |-  ( ( ( ( ( ( ( ph  /\  ch )  /\  th )  /\  ta )  /\  et )  /\  ze )  /\  si )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
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 is referenced by:  ad7antr  492  supinfneg  9416  infsupneg  9417  cvg1nlemres  10788  suplociccreex  12808
  Copyright terms: Public domain W3C validator