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Theorem 19.42vvv 1786
 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 1785 . . 3 (yz(φ ψ) ↔ (φ yzψ))
21exbii 1493 . 2 (xyz(φ ψ) ↔ x(φ yzψ))
3 19.42v 1783 . 2 (x(φ yzψ) ↔ (φ xyzψ))
42, 3bitri 173 1 (xyz(φ ψ) ↔ (φ xyzψ))
 Colors of variables: wff set class Syntax hints:   ∧ wa 97   ↔ wb 98  ∃wex 1378 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-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  ceqsex6v  2592
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