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Theorem ad5ant2345 28544
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant2345.1  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
Assertion
Ref Expression
ad5ant2345  |-  ( ( ( ( ( et 
/\  ph )  /\  ps )  /\  ch )  /\  th )  ->  ta )

Proof of Theorem ad5ant2345
StepHypRef Expression
1 ad5ant2345.1 . . . . 5  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ta )
21exp41 593 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
32a1i 10 . . 3  |-  ( et 
->  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta )
) ) ) )
43imp 418 . 2  |-  ( ( et  /\  ph )  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
54imp41 576 1  |-  ( ( ( ( ( et 
/\  ph )  /\  ps )  /\  ch )  /\  th )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
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 177  df-an 360
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