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Theorem el123 28539
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el123.1  |-  (. ph  ->.  ps
).
el123.2  |-  (. ch  ->.  th
).
el123.3  |-  (. ta  ->.  et
).
el123.4  |-  ( ( ps  /\  th  /\  et )  ->  ze )
Assertion
Ref Expression
el123  |-  (. (. ph ,. ch ,. ta ).  ->.  ze ).

Proof of Theorem el123
StepHypRef Expression
1 el123.1 . . . 4  |-  (. ph  ->.  ps
).
21in1 28339 . . 3  |-  ( ph  ->  ps )
3 el123.2 . . . 4  |-  (. ch  ->.  th
).
43in1 28339 . . 3  |-  ( ch 
->  th )
5 el123.3 . . . 4  |-  (. ta  ->.  et
).
65in1 28339 . . 3  |-  ( ta 
->  et )
7 el123.4 . . 3  |-  ( ( ps  /\  th  /\  et )  ->  ze )
82, 4, 6, 7syl3an 1224 . 2  |-  ( (
ph  /\  ch  /\  ta )  ->  ze )
98dfvd3anir 28365 1  |-  (. (. ph ,. ch ,. ta ).  ->.  ze ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934   (.wvd1 28337   (.wvhc3 28357
This theorem is referenced by:  suctrALTcfVD  28699
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 28338  df-vhc3 28358
  Copyright terms: Public domain W3C validator