Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ecase2d Structured version   Visualization version   Unicode version

Theorem ecase2d 952
 Description: Deduction for elimination by cases. (Contributed by NM, 21-Apr-1994.) (Proof shortened by Wolf Lammen, 22-Dec-2012.)
Hypotheses
Ref Expression
ecase2d.1
ecase2d.2
ecase2d.3
ecase2d.4
Assertion
Ref Expression
ecase2d

Proof of Theorem ecase2d
StepHypRef Expression
1 idd 25 . 2
2 ecase2d.1 . . . 4
3 ecase2d.2 . . . . 5
43pm2.21d 110 . . . 4
52, 4mpand 682 . . 3
6 ecase2d.3 . . . . 5
76pm2.21d 110 . . . 4
82, 7mpand 682 . . 3
95, 8jaod 382 . 2
10 ecase2d.4 . 2
111, 9, 10mpjaod 383 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wo 370   wa 371 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 189  df-or 372  df-an 373 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator