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Theorem gen22 37043
Description: Virtual deduction generalizing rule for two quantifying variables and two virtual hypothesis. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen22.1  |-  (. ph ,. ps  ->.  ch ).
Assertion
Ref Expression
gen22  |-  (. ph ,. ps  ->.  A. x A. y ch ).
Distinct variable groups:    ph, x    ph, y    ps, x    ps, y
Allowed substitution hints:    ch( x, y)

Proof of Theorem gen22
StepHypRef Expression
1 gen22.1 . . . . 5  |-  (. ph ,. ps  ->.  ch ).
21dfvd2i 36997 . . . 4  |-  ( ph  ->  ( ps  ->  ch ) )
32alrimdv 1785 . . 3  |-  ( ph  ->  ( ps  ->  A. y ch ) )
43alrimdv 1785 . 2  |-  ( ph  ->  ( ps  ->  A. x A. y ch ) )
54dfvd2ir 36998 1  |-  (. ph ,. ps  ->.  A. x A. y ch ).
Colors of variables: wff setvar class
Syntax hints:   A.wal 1452   (.wvd2 36989
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768
This theorem depends on definitions:  df-bi 190  df-an 377  df-vd2 36990
This theorem is referenced by: (None)
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