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Theorem ralbid 2632
 Description: Formula-building rule for restricted universal quantifier (deduction rule). (Contributed by NM, 27-Jun-1998.)
Hypotheses
Ref Expression
ralbid.1 xφ
ralbid.2 (φ → (ψχ))
Assertion
Ref Expression
ralbid (φ → (x A ψx A χ))

Proof of Theorem ralbid
StepHypRef Expression
1 ralbid.1 . 2 xφ
2 ralbid.2 . . 3 (φ → (ψχ))
32adantr 451 . 2 ((φ x A) → (ψχ))
41, 3ralbida 2628 1 (φ → (x A ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  Ⅎwnf 1544   ∈ wcel 1710  ∀wral 2614 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-ral 2619 This theorem is referenced by:  ralbidv  2634  sbcralt  3118  sbcrext  3119
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