Theorem ecase3d 984

Description: Deduction for elimination by cases. (Contributed by NM, 2-May-1996.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Hypotheses

Ref	Expression
ecase3d.1	|- ( ph -> ( ps -> th ) )
ecase3d.2	|- ( ph -> ( ch -> th ) )
ecase3d.3	|- ( ph -> ( -. ( ps \/ ch ) -> th ) )

Assertion

Ref	Expression
ecase3d	|- ( ph -> th )

Proof of Theorem ecase3d

Step	Hyp	Ref	Expression
1		ecase3d.1	. . 3 |- ( ph -> ( ps -> th ) )
2		ecase3d.2	. . 3 |- ( ph -> ( ch -> th ) )
3	1, 2	jaod 395	. 2 |- ( ph -> ( ( ps \/ ch ) -> th ) )
4		ecase3d.3	. 2 |- ( ph -> ( -. ( ps \/ ch ) -> th ) )
5	3, 4	pm2.61d 170	1 |- ( ph -> th )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385

This theorem is referenced by:  ecased  985  distrlem4pr  9848  lcmdvds  15321  atcvat4i  29256  cvrat4  34729