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Theorem 2ralimi 2521
Description: Inference quantifying both antecedent and consequent two times, with strong hypothesis. (Contributed by AV, 3-Dec-2021.)
Hypothesis
Ref Expression
ralimi.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
2ralimi  |-  ( A. x  e.  A  A. y  e.  B  ph  ->  A. x  e.  A  A. y  e.  B  ps )

Proof of Theorem 2ralimi
StepHypRef Expression
1 ralimi.1 . . 3  |-  ( ph  ->  ps )
21ralimi 2520 . 2  |-  ( A. y  e.  B  ph  ->  A. y  e.  B  ps )
32ralimi 2520 1  |-  ( A. x  e.  A  A. y  e.  B  ph  ->  A. x  e.  A  A. y  e.  B  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wral 2435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429
This theorem depends on definitions:  df-bi 116  df-ral 2440
This theorem is referenced by:  xmeteq0  12801  xmettri2  12803
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