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Theorem in2an 28380
Description: The virtual deduction introduction rule converting the second conjunct of the second virtual hypothesis into the antecedent of the conclusion. exp3a 425 is the non-virtual deduction form of in2an 28380. (Contributed by Alan Sare, 30-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
in2an.1  |-  (. ph ,. ( ps  /\  ch ) 
->.  th ).
Assertion
Ref Expression
in2an  |-  (. ph ,. ps  ->.  ( ch  ->  th ) ).

Proof of Theorem in2an
StepHypRef Expression
1 in2an.1 . . . 4  |-  (. ph ,. ( ps  /\  ch ) 
->.  th ).
21dfvd2i 28354 . . 3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
32exp3a 425 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
43dfvd2ir 28355 1  |-  (. ph ,. ps  ->.  ( ch  ->  th ) ).
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   (.wvd2 28346
This theorem is referenced by:  onfrALTVD  28667
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-vd2 28347
  Copyright terms: Public domain W3C validator