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Theorem ad5ant125 28730
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant125.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
ad5ant125  |-  ( ( ( ( ( ph  /\ 
ps )  /\  ta )  /\  et )  /\  ch )  ->  th )

Proof of Theorem ad5ant125
StepHypRef Expression
1 ad5ant125.1 . . . . . . 7  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213exp 1153 . . . . . 6  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32a1i4 26341 . . . . 5  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  ->  th ) ) ) )
43a1i4 26341 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( et  ->  ( ta  ->  th )
) ) ) )
54com35 87 . . 3  |-  ( ph  ->  ( ps  ->  ( ta  ->  ( et  ->  ( ch  ->  th )
) ) ) )
65imp 420 . 2  |-  ( (
ph  /\  ps )  ->  ( ta  ->  ( et  ->  ( ch  ->  th ) ) ) )
76imp41 578 1  |-  ( ( ( ( ( ph  /\ 
ps )  /\  ta )  /\  et )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    /\ w3a 937
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  df-3an 939
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