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Theorem anim12dan 542
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 112 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
3 anim12dan.2 . . . 4  |-  ( (
ph  /\  th )  ->  ta )
43ex 112 . . 3  |-  ( ph  ->  ( th  ->  ta ) )
52, 4anim12d 322 . 2  |-  ( ph  ->  ( ( ps  /\  th )  ->  ( ch  /\ 
ta ) ) )
65imp 119 1  |-  ( (
ph  /\  ( ps  /\ 
th ) )  -> 
( ch  /\  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  xpexr2m  4790  isocnv  5479  f1oiso  5493  f1oiso2  5494  f1o2ndf1  5877
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