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Theorem rspe 2485
 Description: Restricted specialization. (Contributed by NM, 12-Oct-1999.)
Assertion
Ref Expression
rspe ((𝑥𝐴𝜑) → ∃𝑥𝐴 𝜑)

Proof of Theorem rspe
StepHypRef Expression
1 19.8a 1570 . 2 ((𝑥𝐴𝜑) → ∃𝑥(𝑥𝐴𝜑))
2 df-rex 2423 . 2 (∃𝑥𝐴 𝜑 ↔ ∃𝑥(𝑥𝐴𝜑))
31, 2sylibr 133 1 ((𝑥𝐴𝜑) → ∃𝑥𝐴 𝜑)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103  ∃wex 1469   ∈ wcel 1481  ∃wrex 2418 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-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488 This theorem depends on definitions:  df-bi 116  df-rex 2423 This theorem is referenced by:  rsp2e  2487  ssiun2  3865  tfrlem9  6225  tfrlemibxssdm  6233  tfr1onlembxssdm  6249  tfrcllembxssdm  6262  findcard2  6792  findcard2s  6793  prarloclemup  7347  prmuloc2  7419  ltaddpr  7449  aptiprlemu  7492  cauappcvgprlemopl  7498  cauappcvgprlemopu  7500  cauappcvgprlem2  7512  caucvgprlemopl  7521  caucvgprlemopu  7523  caucvgprlem2  7532  caucvgprprlem2  7562  suplocexprlemrl  7569  suplocexprlemru  7571  suplocexprlemlub  7576
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