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Theorem vd23 36619
Description: A virtual deduction with 2 virtual hypotheses virtually inferring a virtual conclusion infers that the same conclusion is virtually inferred by the same 2 virtual hypotheses and a third hypothesis. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd23.1  |-  (. ph ,. ps  ->.  ch ).
Assertion
Ref Expression
vd23  |-  (. ph ,. ps ,. th  ->.  ch ).

Proof of Theorem vd23
StepHypRef Expression
1 vd23.1 . . . 4  |-  (. ph ,. ps  ->.  ch ).
21dfvd2i 36593 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32a1dd 47 . 2  |-  ( ph  ->  ( ps  ->  ( th  ->  ch ) ) )
43dfvd3ir 36601 1  |-  (. ph ,. ps ,. th  ->.  ch ).
Colors of variables: wff setvar class
Syntax hints:   (.wvd2 36585   (.wvd3 36595
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 188  df-an 372  df-3an 984  df-vd2 36586  df-vd3 36598
This theorem is referenced by:  e23  36782  e32  36785  e123  36789
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