MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3anim3i Unicode version

Theorem 3anim3i 1139
Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.)
Hypothesis
Ref Expression
3animi.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
3anim3i  |-  ( ( ch  /\  th  /\  ph )  ->  ( ch  /\ 
th  /\  ps )
)

Proof of Theorem 3anim3i
StepHypRef Expression
1 id 19 . 2  |-  ( ch 
->  ch )
2 id 19 . 2  |-  ( th 
->  th )
3 3animi.1 . 2  |-  ( ph  ->  ps )
41, 2, 33anim123i 1137 1  |-  ( ( ch  /\  th  /\  ph )  ->  ( ch  /\ 
th  /\  ps )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem is referenced by:  syl3anl3  1232  syl3anr3  1236  elioo4g  10711  tmdcn2  17772  minvecolem3  21455  axcont  24604  btwnconn1lem4  24713  btwnconn1lem5  24714  btwnconn1lem6  24715  posprsr  25240  bnj556  28932  bnj557  28933  bnj1145  29023
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  df-3an 936
  Copyright terms: Public domain W3C validator