MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  r19.30 Unicode version

Theorem r19.30 3002
Description: Restricted quantifier version of 19.30 1692. (Contributed by Scott Fenton, 25-Feb-2011.)
Assertion
Ref Expression
r19.30

Proof of Theorem r19.30
StepHypRef Expression
1 ralim 2846 . 2
2 orcom 387 . . . 4
3 df-or 370 . . . 4
42, 3bitri 249 . . 3
54ralbii 2888 . 2
6 orcom 387 . . 3
7 dfrex2 2908 . . . 4
87orbi2i 519 . . 3
9 imor 412 . . 3
106, 8, 93bitr4i 277 . 2
111, 5, 103imtr4i 266 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  \/wo 368  A.wral 2807  E.wrex 2808
This theorem is referenced by:  disjunsn  27453  esumcvg  28092
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-ral 2812  df-rex 2813
  Copyright terms: Public domain W3C validator