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Theorem anim12da 29820
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 835 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  -> 
( th  /\  ta ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  ghomco  29964  rngohomco  29996  rngoisocnv  30003  rngoisoco  30004  idlsubcl  30039
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