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Theorem 19.42vvv 1908
 Description: Theorem 19.42 of [Margaris] p. 90 with 3 quantifiers. (Contributed by NM, 21-Sep-2011.)
Assertion
Ref Expression
19.42vvv (xyz(φ ψ) ↔ (φ xyzψ))
Distinct variable groups:   φ,x   φ,y   φ,z
Allowed substitution hints:   ψ(x,y,z)

Proof of Theorem 19.42vvv
StepHypRef Expression
1 19.42vv 1907 . . 3 (yz(φ ψ) ↔ (φ yzψ))
21exbii 1582 . 2 (xyz(φ ψ) ↔ x(φ yzψ))
3 19.42v 1905 . 2 (x(φ yzψ) ↔ (φ xyzψ))
42, 3bitri 240 1 (xyz(φ ψ) ↔ (φ xyzψ))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   ∧ wa 358  ∃wex 1541 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-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by:  ceqsex6v  2899
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