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Theorem ad5ant23 28648
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant23.1  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
ad5ant23  |-  ( ( ( ( ( th 
/\  ph )  /\  ps )  /\  ta )  /\  et )  ->  ch )

Proof of Theorem ad5ant23
StepHypRef Expression
1 ad5ant23.1 . . . . . . . 8  |-  ( (
ph  /\  ps )  ->  ch )
21ex 425 . . . . . . 7  |-  ( ph  ->  ( ps  ->  ch ) )
32a1i34 26340 . . . . . 6  |-  ( ph  ->  ( ps  ->  ( th  ->  ( ta  ->  ch ) ) ) )
43a1i4 26337 . . . . 5  |-  ( ph  ->  ( ps  ->  ( th  ->  ( et  ->  ( ta  ->  ch )
) ) ) )
54com45 86 . . . 4  |-  ( ph  ->  ( ps  ->  ( th  ->  ( ta  ->  ( et  ->  ch )
) ) ) )
65com3r 76 . . 3  |-  ( th 
->  ( ph  ->  ( ps  ->  ( ta  ->  ( et  ->  ch )
) ) ) )
76imp 420 . 2  |-  ( ( th  /\  ph )  ->  ( ps  ->  ( ta  ->  ( et  ->  ch ) ) ) )
87imp41 578 1  |-  ( ( ( ( ( th 
/\  ph )  /\  ps )  /\  ta )  /\  et )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360
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 179  df-an 362
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