Users' Mathboxes Mathbox for Jeff Madsen < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  anim12da Unicode version

Theorem anim12da 26332
Description: Conjoin antecedents and consequents in a deduction. (Contributed by Jeff Madsen, 16-Jun-2011.)
Hypotheses
Ref Expression
anim12da.1  |-  ( (
ph  /\  ps )  ->  th )
anim12da.2  |-  ( (
ph  /\  ch )  ->  ta )
Assertion
Ref Expression
anim12da  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  -> 
( th  /\  ta ) )

Proof of Theorem anim12da
StepHypRef Expression
1 anim12da.1 . 2  |-  ( (
ph  /\  ps )  ->  th )
2 anim12da.2 . 2  |-  ( (
ph  /\  ch )  ->  ta )
31, 2anim12dan 810 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  -> 
( th  /\  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  ghomco  26573  rngohomco  26605  rngoisocnv  26612  rngoisoco  26613  idlsubcl  26648
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
  Copyright terms: Public domain W3C validator