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Theorem el0321old 28804
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el0321old.1  |-  ph
el0321old.2  |-  (. (. ps ,. ch ,. th ).  ->.  ta ).
el0321old.3  |-  ( (
ph  /\  ta )  ->  et )
Assertion
Ref Expression
el0321old  |-  (. (. ps ,. ch ,. th ).  ->.  et ).

Proof of Theorem el0321old
StepHypRef Expression
1 el0321old.1 . . 3  |-  ph
2 el0321old.2 . . . 4  |-  (. (. ps ,. ch ,. th ).  ->.  ta ).
32dfvd3ani 28663 . . 3  |-  ( ( ps  /\  ch  /\  th )  ->  ta )
4 el0321old.3 . . 3  |-  ( (
ph  /\  ta )  ->  et )
51, 3, 4eel0321old 28803 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  et )
65dfvd3anir 28664 1  |-  (. (. ps ,. ch ,. th ).  ->.  et ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd1 28636   (.wvhc3 28656
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-vd1 28637  df-vhc3 28657
  Copyright terms: Public domain W3C validator