Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e111 Unicode version

Theorem e111 28446
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e111.1  |-  (. ph  ->.  ps
).
e111.2  |-  (. ph  ->.  ch
).
e111.3  |-  (. ph  ->.  th
).
e111.4  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
Assertion
Ref Expression
e111  |-  (. ph  ->.  ta
).

Proof of Theorem e111
StepHypRef Expression
1 e111.3 . . . . 5  |-  (. ph  ->.  th
).
21in1 28339 . . . 4  |-  ( ph  ->  th )
3 e111.1 . . . . . . 7  |-  (. ph  ->.  ps
).
43in1 28339 . . . . . 6  |-  ( ph  ->  ps )
5 e111.2 . . . . . . 7  |-  (. ph  ->.  ch
).
65in1 28339 . . . . . 6  |-  ( ph  ->  ch )
7 e111.4 . . . . . 6  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
84, 6, 7syl2im 34 . . . . 5  |-  ( ph  ->  ( ph  ->  ( th  ->  ta ) ) )
98pm2.43i 43 . . . 4  |-  ( ph  ->  ( th  ->  ta ) )
102, 9syl5com 26 . . 3  |-  ( ph  ->  ( ph  ->  ta ) )
1110pm2.43i 43 . 2  |-  ( ph  ->  ta )
1211dfvd1ir 28341 1  |-  (. ph  ->.  ta
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337
This theorem is referenced by:  e110  28448  e101  28450  e011  28452  e100  28454  e010  28456  e001  28458  e11  28460  sbcoreleleqVD  28635  ordelordALTVD  28643
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-vd1 28338
  Copyright terms: Public domain W3C validator