Theorem 3ianorr 1309

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

Step	Hyp	Ref	Expression
1		simp1 997	. . 3 |- ( ( ph /\ ps /\ ch ) -> ph )
2	1	con3i 632	. 2 |- ( -. ph -> -. ( ph /\ ps /\ ch ) )
3		simp2 998	. . 3 |- ( ( ph /\ ps /\ ch ) -> ps )
4	3	con3i 632	. 2 |- ( -. ps -> -. ( ph /\ ps /\ ch ) )
5		simp3 999	. . 3 |- ( ( ph /\ ps /\ ch ) -> ch )
6	5	con3i 632	. 2 |- ( -. ch -> -. ( ph /\ ps /\ ch ) )
7	2, 4, 6	3jaoi 1303	1 |- ( ( -. ph \/ -. ps \/ -. ch ) -> -. ( ph /\ ps /\ ch ) )

Syntax hints:   -. wn 3   -> wi 4   \/ w3o 977   /\ w3a 978

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117  df-3or 979  df-3an 980

This theorem is referenced by:  funtpg  5269