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Theorem reximia 2486
Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 10-Feb-1997.)
Hypothesis
Ref Expression
reximia.1 (𝑥𝐴 → (𝜑𝜓))
Assertion
Ref Expression
reximia (∃𝑥𝐴 𝜑 → ∃𝑥𝐴 𝜓)

Proof of Theorem reximia
StepHypRef Expression
1 rexim 2485 . 2 (∀𝑥𝐴 (𝜑𝜓) → (∃𝑥𝐴 𝜑 → ∃𝑥𝐴 𝜓))
2 reximia.1 . 2 (𝑥𝐴 → (𝜑𝜓))
31, 2mprg 2448 1 (∃𝑥𝐴 𝜑 → ∃𝑥𝐴 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1448  wrex 2376
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-4 1455  ax-ial 1482
This theorem depends on definitions:  df-bi 116  df-ral 2380  df-rex 2381
This theorem is referenced by:  reximi  2488  iunpw  4339  nsmallnqq  7121  1idprl  7299  1idpru  7300  qmulz  9265  zq  9268  caubnd2  10729
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