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Theorem rspec2 2402
Description: Specialization rule for restricted quantification. (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rspec2.1 x A y B φ
Assertion
Ref Expression
rspec2 ((x A y B) → φ)

Proof of Theorem rspec2
StepHypRef Expression
1 rspec2.1 . . 3 x A y B φ
21rspec 2367 . 2 (x Ay B φ)
32r19.21bi 2401 1 ((x A y B) → φ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   wcel 1390  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-ral 2305
This theorem is referenced by:  rspec3  2403  ordtriexmid  4210  onsucsssucexmid  4212
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