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Theorem ad5ant145 27909
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant145.1  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
Assertion
Ref Expression
ad5ant145  |-  ( ( ( ( ( ph  /\ 
ta )  /\  et )  /\  ps )  /\  ch )  ->  th )

Proof of Theorem ad5ant145
StepHypRef Expression
1 ad5ant145.1 . . . . . . . . . . 11  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
213exp 1152 . . . . . . . . . 10  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32a1i4 25992 . . . . . . . . 9  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  ->  th ) ) ) )
43a1i4 25992 . . . . . . . 8  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( et  ->  ( ta  ->  th )
) ) ) )
54com45 85 . . . . . . 7  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  ->  ( et  ->  th )
) ) ) )
65com34 79 . . . . . 6  |-  ( ph  ->  ( ps  ->  ( ta  ->  ( ch  ->  ( et  ->  th )
) ) ) )
76com23 74 . . . . 5  |-  ( ph  ->  ( ta  ->  ( ps  ->  ( ch  ->  ( et  ->  th )
) ) ) )
87com45 85 . . . 4  |-  ( ph  ->  ( ta  ->  ( ps  ->  ( et  ->  ( ch  ->  th )
) ) ) )
98com34 79 . . 3  |-  ( ph  ->  ( ta  ->  ( et  ->  ( ps  ->  ( ch  ->  th )
) ) ) )
109imp 419 . 2  |-  ( (
ph  /\  ta )  ->  ( et  ->  ( ps  ->  ( ch  ->  th ) ) ) )
1110imp41 577 1  |-  ( ( ( ( ( ph  /\ 
ta )  /\  et )  /\  ps )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    /\ w3a 936
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-an 361  df-3an 938
  Copyright terms: Public domain W3C validator