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Theorem ad5ant25 31060
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant25.1  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
ad5ant25  |-  ( ( ( ( ( th 
/\  ph )  /\  ta )  /\  et )  /\  ps )  ->  ch )

Proof of Theorem ad5ant25
StepHypRef Expression
1 ad5ant25.1 . . . . . . . . . 10  |-  ( (
ph  /\  ps )  ->  ch )
21ex 434 . . . . . . . . 9  |-  ( ph  ->  ( ps  ->  ch ) )
32a1i34 28447 . . . . . . . 8  |-  ( ph  ->  ( ps  ->  ( th  ->  ( ta  ->  ch ) ) ) )
43a1i4 28444 . . . . . . 7  |-  ( ph  ->  ( ps  ->  ( th  ->  ( et  ->  ( ta  ->  ch )
) ) ) )
54com45 89 . . . . . 6  |-  ( ph  ->  ( ps  ->  ( th  ->  ( ta  ->  ( et  ->  ch )
) ) ) )
65com3r 79 . . . . 5  |-  ( th 
->  ( ph  ->  ( ps  ->  ( ta  ->  ( et  ->  ch )
) ) ) )
76com34 83 . . . 4  |-  ( th 
->  ( ph  ->  ( ta  ->  ( ps  ->  ( et  ->  ch )
) ) ) )
87com45 89 . . 3  |-  ( th 
->  ( ph  ->  ( ta  ->  ( et  ->  ( ps  ->  ch )
) ) ) )
98imp 429 . 2  |-  ( ( th  /\  ph )  ->  ( ta  ->  ( et  ->  ( ps  ->  ch ) ) ) )
109imp41 593 1  |-  ( ( ( ( ( th 
/\  ph )  /\  ta )  /\  et )  /\  ps )  ->  ch )
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: (None)
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