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Theorem abcdta 27890
Description: Given (((a and b) and c) and d), there exists a proof for a (Contributed by Jarvin Udandy, 3-Sep-2016.)
Hypothesis
Ref Expression
abcdta.1  |-  ( ( ( ph  /\  ps )  /\  ch )  /\  th )
Assertion
Ref Expression
abcdta  |-  ph

Proof of Theorem abcdta
StepHypRef Expression
1 abcdta.1 . . . 4  |-  ( ( ( ph  /\  ps )  /\  ch )  /\  th )
2 simpl 443 . . . 4  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  (
( ph  /\  ps )  /\  ch ) )
31, 2ax-mp 8 . . 3  |-  ( (
ph  /\  ps )  /\  ch )
4 simpl 443 . . 3  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( ph  /\  ps )
)
53, 4ax-mp 8 . 2  |-  ( ph  /\ 
ps )
6 simpl 443 . 2  |-  ( (
ph  /\  ps )  ->  ph )
75, 6ax-mp 8 1  |-  ph
Colors of variables: wff set class
Syntax hints:    /\ 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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