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Theorem r19.32v 2757
 Description: Theorem 19.32 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 25-Nov-2003.)
Assertion
Ref Expression
r19.32v (x A (φ ψ) ↔ (φ x A ψ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem r19.32v
StepHypRef Expression
1 r19.21v 2701 . 2 (x Aφψ) ↔ (¬ φx A ψ))
2 df-or 359 . . 3 ((φ ψ) ↔ (¬ φψ))
32ralbii 2638 . 2 (x A (φ ψ) ↔ x Aφψ))
4 df-or 359 . 2 ((φ x A ψ) ↔ (¬ φx A ψ))
51, 3, 43bitr4i 268 1 (x A (φ ψ) ↔ (φ x A ψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357  ∀wral 2614 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  iinun2  4032  iinuni  4049
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