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Theorem int2 28378
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 28378 is ex 423. (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 28352 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
32ex 423 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
43dfvd1ir 28341 1  |-  (. ph  ->.  ( ps  ->  ch ) ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337   (.wvhc2 28349
This theorem is referenced by:  sspwimpVD  28695  sspwimpcfVD  28697  suctrALTcfVD  28699
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-an 360  df-vd1 28338  df-vhc2 28350
  Copyright terms: Public domain W3C validator