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Theorem e111 33561
Description: A virtual deduction elimination rule (see syl3c 61). (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 33449 . . . 4  |-  ( ph  ->  th )
3 e111.1 . . . . . . 7  |-  (. ph  ->.  ps
).
43in1 33449 . . . . . 6  |-  ( ph  ->  ps )
5 e111.2 . . . . . . 7  |-  (. ph  ->.  ch
).
65in1 33449 . . . . . 6  |-  ( ph  ->  ch )
7 e111.4 . . . . . 6  |-  ( ps 
->  ( ch  ->  ( th  ->  ta ) ) )
84, 6, 7syl2im 38 . . . . 5  |-  ( ph  ->  ( ph  ->  ( th  ->  ta ) ) )
98pm2.43i 47 . . . 4  |-  ( ph  ->  ( th  ->  ta ) )
102, 9syl5com 30 . . 3  |-  ( ph  ->  ( ph  ->  ta ) )
1110pm2.43i 47 . 2  |-  ( ph  ->  ta )
1211dfvd1ir 33451 1  |-  (. ph  ->.  ta
).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 33447
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 185  df-vd1 33448
This theorem is referenced by:  e110  33563  e101  33565  e011  33567  e100  33569  e010  33571  e001  33573  e11  33575  sbcoreleleqVD  33760  ordelordALTVD  33768
  Copyright terms: Public domain W3C validator