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Theorem rsp2e 2891
Description: Restricted specialization. (Contributed by FL, 4-Jun-2012.) (Proof shortened by Wolf Lammen, 7-Jan-2020.)
Assertion
Ref Expression
rsp2e  |-  ( ( x  e.  A  /\  y  e.  B  /\  ph )  ->  E. x  e.  A  E. y  e.  B  ph )

Proof of Theorem rsp2e
StepHypRef Expression
1 rspe 2890 . . 3  |-  ( ( y  e.  B  /\  ph )  ->  E. y  e.  B  ph )
2 rspe 2890 . . 3  |-  ( ( x  e.  A  /\  E. y  e.  B  ph )  ->  E. x  e.  A  E. y  e.  B  ph )
31, 2sylan2 476 . 2  |-  ( ( x  e.  A  /\  ( y  e.  B  /\  ph ) )  ->  E. x  e.  A  E. y  e.  B  ph )
433impb 1201 1  |-  ( ( x  e.  A  /\  y  e.  B  /\  ph )  ->  E. x  e.  A  E. y  e.  B  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 370    /\ w3a 982    e. wcel 1870   E.wrex 2783
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-12 1907
This theorem depends on definitions:  df-bi 188  df-an 372  df-3an 984  df-ex 1660  df-rex 2788
This theorem is referenced by:  pell14qrdich  35422
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