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Theorem el021old 36511
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el021old.1  |-  ph
el021old.2  |-  (. (. ps ,. ch ).  ->.  th ).
el021old.3  |-  ( (
ph  /\  th )  ->  ta )
Assertion
Ref Expression
el021old  |-  (. (. ps ,. ch ).  ->.  ta ).

Proof of Theorem el021old
StepHypRef Expression
1 el021old.1 . . 3  |-  ph
2 el021old.2 . . . 4  |-  (. (. ps ,. ch ).  ->.  th ).
32dfvd2ani 36384 . . 3  |-  ( ( ps  /\  ch )  ->  th )
4 el021old.3 . . 3  |-  ( (
ph  /\  th )  ->  ta )
51, 3, 4sylancr 661 . 2  |-  ( ( ps  /\  ch )  ->  ta )
65dfvd2anir 36385 1  |-  (. (. ps ,. ch ).  ->.  ta ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   (.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-vd1 36371  df-vhc2 36382
This theorem is referenced by:  sspwimpcfVD  36752  suctrALTcfVD  36754
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