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Theorem rexbid 2299
 Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 27-Jun-1998.)
Hypotheses
Ref Expression
ralbid.1 xφ
ralbid.2 (φ → (ψχ))
Assertion
Ref Expression
rexbid (φ → (x A ψx A χ))

Proof of Theorem rexbid
StepHypRef Expression
1 ralbid.1 . 2 xφ
2 ralbid.2 . . 3 (φ → (ψχ))
32adantr 261 . 2 ((φ x A) → (ψχ))
41, 3rexbida 2295 1 (φ → (x A ψx A χ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 98  Ⅎwnf 1325   ∈ wcel 1370  ∃wrex 2281 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-4 1377  ax-ial 1405 This theorem depends on definitions:  df-bi 110  df-nf 1326  df-rex 2286 This theorem is referenced by:  rexbidv  2301  sbcrext  2808  sscoll2  7345
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