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Theorem ral2imi 2428
Description: Inference quantifying antecedent, nested antecedent, and consequent, with a strong hypothesis. (Contributed by NM, 19-Dec-2006.)
Hypothesis
Ref Expression
ral2imi.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
ral2imi  |-  ( A. x  e.  A  ph  ->  ( A. x  e.  A  ps  ->  A. x  e.  A  ch ) )

Proof of Theorem ral2imi
StepHypRef Expression
1 ral2imi.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21ralimi 2427 . 2  |-  ( A. x  e.  A  ph  ->  A. x  e.  A  ( ps  ->  ch )
)
3 ralim 2423 . 2  |-  ( A. x  e.  A  ( ps  ->  ch )  -> 
( A. x  e.  A  ps  ->  A. x  e.  A  ch )
)
42, 3syl 14 1  |-  ( A. x  e.  A  ph  ->  ( A. x  e.  A  ps  ->  A. x  e.  A  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wral 2349
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379
This theorem depends on definitions:  df-bi 115  df-ral 2354
This theorem is referenced by:  r19.26  2486  iinerm  6244  bj-findis  10932
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