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Theorem rexbidva 2631
 Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 9-Mar-1997.)
Hypothesis
Ref Expression
ralbidva.1 ((φ x A) → (ψχ))
Assertion
Ref Expression
rexbidva (φ → (x A ψx A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem rexbidva
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 ralbidva.1 . 2 ((φ x A) → (ψχ))
31, 2rexbida 2629 1 (φ → (x A ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   ∈ wcel 1710  ∃wrex 2615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-rex 2620 This theorem is referenced by:  2rexbiia  2648  2rexbidva  2655  rexeqbidva  2822  phidisjnn  4615  phialllem1  4616  dfimafn  5366  funimass4  5368  fconstfv  5456  isomin  5496  f1oiso  5499
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