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Theorem ralrimivvva 2707
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version with triple quantification.) (Contributed by Mario Carneiro, 9-Jul-2014.)
Hypothesis
Ref Expression
ralrimivvva.1 ((φ (x A y B z C)) → ψ)
Assertion
Ref Expression
ralrimivvva (φx A y B z C ψ)
Distinct variable groups:   φ,x,y,z   y,A,z   z,B
Allowed substitution hints:   ψ(x,y,z)   A(x)   B(x,y)   C(x,y,z)

Proof of Theorem ralrimivvva
StepHypRef Expression
1 ralrimivvva.1 . . . . . 6 ((φ (x A y B z C)) → ψ)
213exp2 1169 . . . . 5 (φ → (x A → (y B → (z Cψ))))
32imp41 576 . . . 4 ((((φ x A) y B) z C) → ψ)
43ralrimiva 2697 . . 3 (((φ x A) y B) → z C ψ)
54ralrimiva 2697 . 2 ((φ x A) → y B z C ψ)
65ralrimiva 2697 1 (φx A y B z C ψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934   ∈ wcel 1710  ∀wral 2614 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-ex 1542  df-nf 1545  df-ral 2619 This theorem is referenced by:  caovassg  5626  caovdig  5632  caovdirg  5633
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