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Theorem 19.41vvv 1903
 Description: Theorem 19.41 of [Margaris] p. 90 with 3 quantifiers. (Contributed by NM, 30-Apr-1995.)
Assertion
Ref Expression
19.41vvv (xyz(φ ψ) ↔ (xyzφ ψ))
Distinct variable groups:   ψ,x   ψ,y   ψ,z
Allowed substitution hints:   φ(x,y,z)

Proof of Theorem 19.41vvv
StepHypRef Expression
1 19.41vv 1902 . . 3 (yz(φ ψ) ↔ (yzφ ψ))
21exbii 1582 . 2 (xyz(φ ψ) ↔ x(yzφ ψ))
3 19.41v 1901 . 2 (x(yzφ ψ) ↔ (xyzφ ψ))
42, 3bitri 240 1 (xyz(φ ψ) ↔ (xyzφ ψ))
 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:  19.41vvvv  1904  eloprabga  5578
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