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Theorem el2122old 36538
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 36384 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
3 el2122old.2 . . . 4  |-  (. ps  ->.  th
).
43in1 36372 . . 3  |-  ( ps 
->  th )
5 el2122old.3 . . . 4  |-  (. ps  ->.  ta
).
65in1 36372 . . 3  |-  ( ps 
->  ta )
7 el2122old.4 . . 3  |-  ( ( ch  /\  th  /\  ta )  ->  et )
82, 4, 6, 7eel2122old 36537 . 2  |-  ( (
ph  /\  ps )  ->  et )
98dfvd2anir 36385 1  |-  (. (. ph ,. ps ).  ->.  et ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ w3a 974   (.wvd1 36370   (.wvhc2 36381
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-an 369  df-3an 976  df-vd1 36371  df-vhc2 36382
This theorem is referenced by:  suctrALTcfVD  36754
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