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Theorem anim12dan 600
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 115 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 anim12dan.2 . . . 4  |-  ( (
ph  /\  th )  ->  ta )
43ex 115 . . 3  |-  ( ph  ->  ( th  ->  ta ) )
52, 4anim12d 335 . 2  |-  ( ph  ->  ( ( ps  /\  th )  ->  ( ch  /\ 
ta ) ) )
65imp 124 1  |-  ( (
ph  /\  ( ps  /\ 
th ) )  -> 
( ch  /\  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  xpexr2m  5085  isocnv  5828  f1oiso  5843  f1oiso2  5844  f1o2ndf1  6247  xpf1o  6862  pc11  12348  imasaddfnlemg  12757  imasaddflemg  12759  mhmpropd  12884  ghmsub  13151  invrpropdg  13460  tgclb  13949  innei  14047  txcn  14159  lgsdir2  14818
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