ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anim12dan Unicode version

Theorem anim12dan 595
Description: Conjoin antecedents and consequents in a deduction. (Contributed by Mario Carneiro, 12-May-2014.)
Hypotheses
Ref Expression
anim12dan.1  |-  ( (
ph  /\  ps )  ->  ch )
anim12dan.2  |-  ( (
ph  /\  th )  ->  ta )
Assertion
Ref Expression
anim12dan  |-  ( (
ph  /\  ( ps  /\ 
th ) )  -> 
( ch  /\  ta ) )

Proof of Theorem anim12dan
StepHypRef Expression
1 anim12dan.1 . . . 4  |-  ( (
ph  /\  ps )  ->  ch )
21ex 114 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 anim12dan.2 . . . 4  |-  ( (
ph  /\  th )  ->  ta )
43ex 114 . . 3  |-  ( ph  ->  ( th  ->  ta ) )
52, 4anim12d 333 . 2  |-  ( ph  ->  ( ( ps  /\  th )  ->  ( ch  /\ 
ta ) ) )
65imp 123 1  |-  ( (
ph  /\  ( ps  /\ 
th ) )  -> 
( ch  /\  ta ) )
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 depends on definitions:  df-bi 116
This theorem is referenced by:  xpexr2m  5050  isocnv  5787  f1oiso  5802  f1oiso2  5803  f1o2ndf1  6204  xpf1o  6818  pc11  12271  mhmpropd  12676  tgclb  12818  innei  12916  txcn  13028  lgsdir2  13687
  Copyright terms: Public domain W3C validator