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Theorem dfvd1ir 28640
Description: Inference form of df-vd1 28637 with the virtual deduction as the assertion. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd1ir.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
dfvd1ir  |-  (. ph  ->.  ps
).

Proof of Theorem dfvd1ir
StepHypRef Expression
1 dfvd1ir.1 . 2  |-  ( ph  ->  ps )
2 df-vd1 28637 . 2  |-  ( (.
ph 
->.  ps ).  <->  ( ph  ->  ps ) )
31, 2mpbir 200 1  |-  (. ph  ->.  ps
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28636
This theorem is referenced by:  idn1  28641  vd01  28674  in2  28682  int2  28683  gen11nv  28694  gen12  28695  exinst01  28702  exinst11  28703  e1_  28704  el1  28705  e111  28751  e1111  28752  un0.1  28868  un10  28877  un01  28878  2uasbanhVD  29003
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 28637
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