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Theorem in3an 27756
Description: The virtual deduction introduction rule converting the second conjunct of the third virtual hypothesis into the antecedent of the conclusion. exp4a 589 is the non-virtual deduction form of in3an 27756. (Contributed by Alan Sare, 25-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
in3an.1  |-  (. ph ,. ps ,. ( ch 
/\  th )  ->.  ta ).
Assertion
Ref Expression
in3an  |-  (. ph ,. ps ,. ch  ->.  ( th  ->  ta ) ).

Proof of Theorem in3an
StepHypRef Expression
1 in3an.1 . . . 4  |-  (. ph ,. ps ,. ( ch 
/\  th )  ->.  ta ).
21dfvd3i 27734 . . 3  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
32exp4a 589 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
43dfvd3ir 27735 1  |-  (. ph ,. ps ,. ch  ->.  ( th  ->  ta ) ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd3 27729
This theorem is referenced by:  onfrALTlem2VD  28038
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-vd3 27732
  Copyright terms: Public domain W3C validator