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Theorem rspec2 2519
Description: Specialization rule for restricted quantification. (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rspec2.1 𝑥𝐴𝑦𝐵 𝜑
Assertion
Ref Expression
rspec2 ((𝑥𝐴𝑦𝐵) → 𝜑)

Proof of Theorem rspec2
StepHypRef Expression
1 rspec2.1 . . 3 𝑥𝐴𝑦𝐵 𝜑
21rspec 2482 . 2 (𝑥𝐴 → ∀𝑦𝐵 𝜑)
32r19.21bi 2518 1 ((𝑥𝐴𝑦𝐵) → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wcel 1480  wral 2414
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-4 1487
This theorem depends on definitions:  df-bi 116  df-ral 2419
This theorem is referenced by:  rspec3  2520  ordtriexmid  4432  onsucsssucexmid  4437
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