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Theorem r19.26-3 2748
 Description: Theorem 19.26 of [Margaris] p. 90 with 3 restricted quantifiers. (Contributed by FL, 22-Nov-2010.)
Assertion
Ref Expression
r19.26-3 (x A (φ ψ χ) ↔ (x A φ x A ψ x A χ))

Proof of Theorem r19.26-3
StepHypRef Expression
1 df-3an 936 . . 3 ((φ ψ χ) ↔ ((φ ψ) χ))
21ralbii 2638 . 2 (x A (φ ψ χ) ↔ x A ((φ ψ) χ))
3 r19.26 2746 . 2 (x A ((φ ψ) χ) ↔ (x A (φ ψ) x A χ))
4 r19.26 2746 . . . 4 (x A (φ ψ) ↔ (x A φ x A ψ))
54anbi1i 676 . . 3 ((x A (φ ψ) x A χ) ↔ ((x A φ x A ψ) x A χ))
6 df-3an 936 . . 3 ((x A φ x A ψ x A χ) ↔ ((x A φ x A ψ) x A χ))
75, 6bitr4i 243 . 2 ((x A (φ ψ) x A χ) ↔ (x A φ x A ψ x A χ))
82, 3, 73bitri 262 1 (x A (φ ψ χ) ↔ (x A φ x A ψ x A χ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358   ∧ w3a 934  ∀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-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by: (None)
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