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Theorem int2 33493
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 33493 is ex 434. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
int2.1  |-  (. (. ph ,. ps ).  ->.  ch ).
Assertion
Ref Expression
int2  |-  (. ph  ->.  ( ps  ->  ch ) ).

Proof of Theorem int2
StepHypRef Expression
1 int2.1 . . . 4  |-  (. (. ph ,. ps ).  ->.  ch ).
21dfvd2ani 33461 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
32ex 434 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
43dfvd1ir 33451 1  |-  (. ph  ->.  ( ps  ->  ch ) ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 33447   (.wvhc2 33458
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 371  df-vd1 33448  df-vhc2 33459
This theorem is referenced by:  sspwimpVD  33820  sspwimpcfVD  33822  suctrALTcfVD  33824
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