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Theorem gen31 28698
Description: Virtual deduction generalizing rule for 1 quantifying variable and 3 virtual hypothesis. gen31 28698 is ggen31 28609 with virtual deductions. (Contributed by Alan Sare, 22-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen31.1  |-  (. ph ,. ps ,. ch  ->.  th ).
Assertion
Ref Expression
gen31  |-  (. ph ,. ps ,. ch  ->.  A. x th ).
Distinct variable groups:    ch, x    ph, x    ps, x
Allowed substitution hint:    th( x)

Proof of Theorem gen31
StepHypRef Expression
1 gen31.1 . . . 4  |-  (. ph ,. ps ,. ch  ->.  th ).
21dfvd3i 28660 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32ggen31 28609 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  A. x th )
) )
43dfvd3ir 28661 1  |-  (. ph ,. ps ,. ch  ->.  A. x th ).
Colors of variables: wff set class
Syntax hints:   A.wal 1530   (.wvd3 28655
This theorem is referenced by:  onfrALTlem2VD  28981
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-vd3 28658
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