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Theorem vd12 36410
Description: A virtual deduction with 1 virtual hypothesis virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same virtual hypothesis and an additional hypothesis. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd12.1  |-  (. ph  ->.  ps
).
Assertion
Ref Expression
vd12  |-  (. ph ,. ch  ->.  ps ).

Proof of Theorem vd12
StepHypRef Expression
1 vd12.1 . . . 4  |-  (. ph  ->.  ps
).
21in1 36372 . . 3  |-  ( ph  ->  ps )
32a1d 25 . 2  |-  ( ph  ->  ( ch  ->  ps ) )
43dfvd2ir 36387 1  |-  (. ph ,. ch  ->.  ps ).
Colors of variables: wff setvar class
Syntax hints:   (.wvd1 36370   (.wvd2 36378
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-vd2 36379
This theorem is referenced by:  e221  36459  e212  36461  e122  36463  e112  36464  e121  36466  e211  36467  e120  36473  e12  36545  e21  36551
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