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Theorem ggen31 36954
Description: gen31 37042 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ggen31.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
ggen31  |-  ( ph  ->  ( ps  ->  ( ch  ->  A. x th )
) )
Distinct variable groups:    ch, x    ph, x    ps, x
Allowed substitution hint:    th( x)

Proof of Theorem ggen31
StepHypRef Expression
1 ggen31.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
21imp 435 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
32alrimdv 1785 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  ->  A. x th ) )
43ex 440 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  A. x th )
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 375   A.wal 1452
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
This theorem is referenced by:  onfrALTlem2  36955  gen31  37042
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