Theorem ecase23d 1361

Description: Variation of ecased 1360 with three disjuncts instead of two. (Contributed by NM, 22-Apr-1994.) (Revised by Jim Kingdon, 9-Dec-2017.)

Hypotheses

Ref	Expression
ecase23d.1	|- ( ph -> -. ch )
ecase23d.2	|- ( ph -> -. th )
ecase23d.3	|- ( ph -> ( ps \/ ch \/ th ) )

Assertion

Ref	Expression
ecase23d	|- ( ph -> ps )

Proof of Theorem ecase23d

Step	Hyp	Ref	Expression
1		ecase23d.1	. 2 |- ( ph -> -. ch )
2		ecase23d.2	. . 3 |- ( ph -> -. th )
3		ecase23d.3	. . . 4 |- ( ph -> ( ps \/ ch \/ th ) )
4		df-3or 981	. . . 4 |- ( ( ps \/ ch \/ th ) <-> ( ( ps \/ ch ) \/ th ) )
5	3, 4	sylib 122	. . 3 |- ( ph -> ( ( ps \/ ch ) \/ th ) )
6	2, 5	ecased 1360	. 2 |- ( ph -> ( ps \/ ch ) )
7	1, 6	ecased 1360	1 |- ( ph -> ps )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 709   \/ w3o 979

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-in2 616  ax-io 710

This theorem depends on definitions:  df-bi 117  df-3or 981

This theorem is referenced by:  iseqf1olemklt  10590  xrmaxiflemcl  11410  xrmaxifle  11411  xrmaxiflemab  11412  xrmaxiflemlub  11413  ennnfonelemex  12631  mulgval  13252  mulgfng  13254  subgmulg  13318