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Theorem 3ianorr 1241
Description: Triple disjunction implies negated triple conjunction. (Contributed by Jim Kingdon, 23-Dec-2018.)
Assertion
Ref Expression
3ianorr  |-  ( ( -.  ph  \/  -.  ps  \/  -.  ch )  ->  -.  ( ph  /\  ps  /\  ch ) )

Proof of Theorem 3ianorr
StepHypRef Expression
1 simp1 939 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ph )
21con3i 595 . 2  |-  ( -. 
ph  ->  -.  ( ph  /\ 
ps  /\  ch )
)
3 simp2 940 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ps )
43con3i 595 . 2  |-  ( -. 
ps  ->  -.  ( ph  /\ 
ps  /\  ch )
)
5 simp3 941 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ch )
65con3i 595 . 2  |-  ( -. 
ch  ->  -.  ( ph  /\ 
ps  /\  ch )
)
72, 4, 63jaoi 1235 1  |-  ( ( -.  ph  \/  -.  ps  \/  -.  ch )  ->  -.  ( ph  /\  ps  /\  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ w3o 919    /\ w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115  df-3or 921  df-3an 922
This theorem is referenced by:  funtpg  4981
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