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Theorem r19.26-3 2437
 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 886 . . 3 ((φ ψ χ) ↔ ((φ ψ) χ))
21ralbii 2324 . 2 (x A (φ ψ χ) ↔ x A ((φ ψ) χ))
3 r19.26 2435 . 2 (x A ((φ ψ) χ) ↔ (x A (φ ψ) x A χ))
4 r19.26 2435 . . . 4 (x A (φ ψ) ↔ (x A φ x A ψ))
54anbi1i 431 . . 3 ((x A (φ ψ) x A χ) ↔ ((x A φ x A ψ) x A χ))
6 df-3an 886 . . 3 ((x A φ x A ψ x A χ) ↔ ((x A φ x A ψ) x A χ))
75, 6bitr4i 176 . 2 ((x A (φ ψ) x A χ) ↔ (x A φ x A ψ x A χ))
82, 3, 73bitri 195 1 (x A (φ ψ χ) ↔ (x A φ x A ψ x A χ))
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ↔ wb 98   ∧ w3a 884  ∀wral 2300 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 1333  ax-gen 1335  ax-4 1397  ax-17 1416 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-ral 2305 This theorem is referenced by: (None)
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