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Theorem int3 37059
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 37059 is 3expia 1233. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
int3.1  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
Assertion
Ref Expression
int3  |-  (. (. ph ,. ps ).  ->.  ( ch  ->  th ) ).

Proof of Theorem int3
StepHypRef Expression
1 int3.1 . . . 4  |-  (. (. ph ,. ps ,. ch ).  ->.  th ).
21dfvd3ani 37033 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
323expia 1233 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
43dfvd2anir 37022 1  |-  (. (. ph ,. ps ).  ->.  ( ch  ->  th ) ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 37007   (.wvhc2 37018   (.wvhc3 37026
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 190  df-an 378  df-3an 1009  df-vd1 37008  df-vhc2 37019  df-vhc3 37027
This theorem is referenced by:  suctrALTcfVD  37383
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