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Theorem int3 28384
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. Conventional form of int3 28384 is 3expia 1153. (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 28364 . . 3  |-  ( (
ph  /\  ps  /\  ch )  ->  th )
323expia 1153 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
43dfvd2anir 28353 1  |-  (. (. ph ,. ps ).  ->.  ( ch  ->  th ) ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   (.wvd1 28337   (.wvhc2 28349   (.wvhc3 28357
This theorem is referenced by:  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-3an 936  df-vd1 28338  df-vhc2 28350  df-vhc3 28358
  Copyright terms: Public domain W3C validator