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Theorem el1 28400
Description: A Virtual deduction elimination rule. syl 15 is el1 28400 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
el1.1  |-  (. ph  ->.  ps
).
el1.2  |-  ( ps 
->  ch )
Assertion
Ref Expression
el1  |-  (. ph  ->.  ch
).

Proof of Theorem el1
StepHypRef Expression
1 el1.1 . . . 4  |-  (. ph  ->.  ps
).
21in1 28339 . . 3  |-  ( ph  ->  ps )
3 el1.2 . . 3  |-  ( ps 
->  ch )
42, 3syl 15 . 2  |-  ( ph  ->  ch )
54dfvd1ir 28341 1  |-  (. ph  ->.  ch
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337
This theorem is referenced by:  sspwimpVD  28695  sspwimpcfVD  28697  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-vd1 28338
  Copyright terms: Public domain W3C validator