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Theorem gen31 36431
Description: Virtual deduction generalizing rule for 1 quantifying variable and 3 virtual hypothesis. gen31 36431 is ggen31 36341 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 36393 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32ggen31 36341 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  A. x th )
) )
43dfvd3ir 36394 1  |-  (. ph ,. ps ,. ch  ->.  A. x th ).
Colors of variables: wff setvar class
Syntax hints:   A.wal 1403   (.wvd3 36388
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725
This theorem depends on definitions:  df-bi 185  df-an 369  df-3an 976  df-vd3 36391
This theorem is referenced by:  onfrALTlem2VD  36720
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