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Theorem exdistr2 1909
Description: Distribution of existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exdistr2 (xyz(φ ψ) ↔ x(φ yzψ))
Distinct variable groups:   φ,y   φ,z
Allowed substitution hints:   φ(x)   ψ(x,y,z)

Proof of Theorem exdistr2
StepHypRef Expression
1 19.42vv 1907 . 2 (yz(φ ψ) ↔ (φ yzψ))
21exbii 1582 1 (xyz(φ ψ) ↔ x(φ yzψ))
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: (None)
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