MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.43OLD Structured version   Unicode version

Theorem 19.43OLD 1699
Description: Obsolete proof of 19.43 1698 as of 3-May-2099. Leave this in for the example on the mmrecent.html page and in conventions 25325. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
19.43OLD  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )

Proof of Theorem 19.43OLD
StepHypRef Expression
1 ioran 488 . . . . 5  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
21albii 1645 . . . 4  |-  ( A. x  -.  ( ph  \/  ps )  <->  A. x ( -. 
ph  /\  -.  ps )
)
3 19.26 1685 . . . 4  |-  ( A. x ( -.  ph  /\ 
-.  ps )  <->  ( A. x  -.  ph  /\  A. x  -.  ps ) )
4 alnex 1619 . . . . 5  |-  ( A. x  -.  ph  <->  -.  E. x ph )
5 alnex 1619 . . . . 5  |-  ( A. x  -.  ps  <->  -.  E. x ps )
64, 5anbi12i 695 . . . 4  |-  ( ( A. x  -.  ph  /\ 
A. x  -.  ps ) 
<->  ( -.  E. x ph  /\  -.  E. x ps ) )
72, 3, 63bitri 271 . . 3  |-  ( A. x  -.  ( ph  \/  ps )  <->  ( -.  E. x ph  /\  -.  E. x ps ) )
87notbii 294 . 2  |-  ( -. 
A. x  -.  ( ph  \/  ps )  <->  -.  ( -.  E. x ph  /\  -.  E. x ps )
)
9 df-ex 1618 . 2  |-  ( E. x ( ph  \/  ps )  <->  -.  A. x  -.  ( ph  \/  ps ) )
10 oran 494 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  -.  ( -.  E. x ph  /\  -.  E. x ps )
)
118, 9, 103bitr4i 277 1  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 366    /\ wa 367   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-ex 1618
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator