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Theorem abcdtb 27891
Description: Given (((a and b) and c) and d), there exists a proof for b (Contributed by Jarvin Udandy, 3-Sep-2016.)
Hypothesis
Ref Expression
abcdtb.1  |-  ( ( ( ph  /\  ps )  /\  ch )  /\  th )
Assertion
Ref Expression
abcdtb  |-  ps

Proof of Theorem abcdtb
StepHypRef Expression
1 abcdtb.1 . . . . 5  |-  ( ( ( ph  /\  ps )  /\  ch )  /\  th )
2 simpl 443 . . . . 5  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  (
( ph  /\  ps )  /\  ch ) )
31, 2ax-mp 8 . . . 4  |-  ( (
ph  /\  ps )  /\  ch )
4 simpl 443 . . . 4  |-  ( ( ( ph  /\  ps )  /\  ch )  -> 
( ph  /\  ps )
)
53, 4ax-mp 8 . . 3  |-  ( ph  /\ 
ps )
6 pm3.22 436 . . 3  |-  ( (
ph  /\  ps )  ->  ( ps  /\  ph ) )
75, 6ax-mp 8 . 2  |-  ( ps 
/\  ph )
8 simpl 443 . 2  |-  ( ( ps  /\  ph )  ->  ps )
97, 8ax-mp 8 1  |-  ps
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
  Copyright terms: Public domain W3C validator