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Theorem dfvd1ir 27998
Description: Inference form of df-vd1 27995 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 27995 . 2  |-  ( (.
ph 
->.  ps ).  <->  ( ph  ->  ps ) )
31, 2mpbir 201 1  |-  (. ph  ->.  ps
).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 27994
This theorem is referenced by:  idn1  27999  vd01  28032  in2  28040  int2  28041  gen11nv  28052  gen12  28053  exinst01  28060  exinst11  28061  e1_  28062  el1  28063  e111  28109  e1111  28110  un0.1  28225  un10  28234  un01  28235  2uasbanhVD  28357
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 178  df-vd1 27995
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