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Theorem pm2.61iii 159
Description: Inference eliminating three antecedents. (Contributed by NM, 2-Jan-2002.) (Proof shortened by Wolf Lammen, 22-Sep-2013.)
Hypotheses
Ref Expression
pm2.61iii.1  |-  ( -. 
ph  ->  ( -.  ps  ->  ( -.  ch  ->  th ) ) )
pm2.61iii.2  |-  ( ph  ->  th )
pm2.61iii.3  |-  ( ps 
->  th )
pm2.61iii.4  |-  ( ch 
->  th )
Assertion
Ref Expression
pm2.61iii  |-  th

Proof of Theorem pm2.61iii
StepHypRef Expression
1 pm2.61iii.4 . 2  |-  ( ch 
->  th )
2 pm2.61iii.1 . . 3  |-  ( -. 
ph  ->  ( -.  ps  ->  ( -.  ch  ->  th ) ) )
3 pm2.61iii.2 . . . 4  |-  ( ph  ->  th )
43a1d 22 . . 3  |-  ( ph  ->  ( -.  ch  ->  th ) )
5 pm2.61iii.3 . . . 4  |-  ( ps 
->  th )
65a1d 22 . . 3  |-  ( ps 
->  ( -.  ch  ->  th ) )
72, 4, 6pm2.61ii 157 . 2  |-  ( -. 
ch  ->  th )
81, 7pm2.61i 156 1  |-  th
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  axrepnd  8216  axacndlem4  8232  axacndlem5  8233  axacnd  8234  nbssntrs  26147
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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