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Theorem el2122old 28806
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el2122old.1  |-  (. (. ph ,. ps ).  ->.  ch ).
el2122old.2  |-  (. ps  ->.  th
).
el2122old.3  |-  (. ps  ->.  ta
).
el2122old.4  |-  ( ( ch  /\  th  /\  ta )  ->  et )
Assertion
Ref Expression
el2122old  |-  (. (. ph ,. ps ).  ->.  et ).

Proof of Theorem el2122old
StepHypRef Expression
1 el2122old.1 . . . 4  |-  (. (. ph ,. ps ).  ->.  ch ).
21dfvd2ani 28651 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
3 el2122old.2 . . . 4  |-  (. ps  ->.  th
).
43in1 28638 . . 3  |-  ( ps 
->  th )
5 el2122old.3 . . . 4  |-  (. ps  ->.  ta
).
65in1 28638 . . 3  |-  ( ps 
->  ta )
7 el2122old.4 . . 3  |-  ( ( ch  /\  th  /\  ta )  ->  et )
82, 4, 6, 7eel2122old 28805 . 2  |-  ( (
ph  /\  ps )  ->  et )
98dfvd2anir 28652 1  |-  (. (. ph ,. ps ).  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934   (.wvd1 28636   (.wvhc2 28648
This theorem is referenced by:  suctrALTcfVD  29015
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-an 360  df-3an 936  df-vd1 28637  df-vhc2 28649
  Copyright terms: Public domain W3C validator