Theorem 3mix1 1161

Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

Ref	Expression
3mix1	|- ( ph -> ( ph \/ ps \/ ch ) )

Proof of Theorem 3mix1

Step	Hyp	Ref	Expression
1		orc 707	. 2 |- ( ph -> ( ph \/ ( ps \/ ch ) ) )
2		3orass 976	. 2 |- ( ( ph \/ ps \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
3	1, 2	sylibr 133	1 |- ( ph -> ( ph \/ ps \/ ch ) )

Syntax hints:   -> wi 4   \/ wo 703   \/ w3o 972

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-io 704

This theorem depends on definitions:  df-bi 116  df-3or 974

This theorem is referenced by:  3mix2  1162  3mix3  1163  3mix1i  1164  3mix1d  1167  3jaob  1297  nntri3or  6472  exmidontriimlem3  7200  elnn0z  9225  nn0le2is012  9294  nn01to3  9576  fztri3or  9995  zabsle1  13694