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Theorem 3ianorr 1272
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 966 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ph )
21con3i 606 . 2  |-  ( -. 
ph  ->  -.  ( ph  /\ 
ps  /\  ch )
)
3 simp2 967 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ps )
43con3i 606 . 2  |-  ( -. 
ps  ->  -.  ( ph  /\ 
ps  /\  ch )
)
5 simp3 968 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  ch )
65con3i 606 . 2  |-  ( -. 
ch  ->  -.  ( ph  /\ 
ps  /\  ch )
)
72, 4, 63jaoi 1266 1  |-  ( ( -.  ph  \/  -.  ps  \/  -.  ch )  ->  -.  ( ph  /\  ps  /\  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ w3o 946    /\ w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-3or 948  df-3an 949
This theorem is referenced by:  funtpg  5144
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