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Theorem ggen31 28633
Description: gen31 28724 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 420 . . 3  |-  ( (
ph  /\  ps )  ->  ( ch  ->  th )
)
32alrimdv 1644 . 2  |-  ( (
ph  /\  ps )  ->  ( ch  ->  A. x th ) )
43ex 425 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  A. x th )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360   A.wal 1550
This theorem is referenced by:  onfrALTlem2  28634  gen31  28724
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627
This theorem depends on definitions:  df-bi 179  df-an 362
  Copyright terms: Public domain W3C validator