Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  el021old Unicode version

Theorem el021old 28779
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 28651 . . 3  |-  ( ( ps  /\  ch )  ->  th )
4 el021old.3 . . 3  |-  ( (
ph  /\  th )  ->  ta )
51, 3, 4sylancr 644 . 2  |-  ( ( ps  /\  ch )  ->  ta )
65dfvd2anir 28652 1  |-  (. (. ps ,. ch ).  ->.  ta ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd1 28636   (.wvhc2 28648
This theorem is referenced by:  sspwimpcfVD  29013  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-vhc2 28649
  Copyright terms: Public domain W3C validator