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Theorem 2ralbidva 2654
Description: Formula-building rule for restricted universal quantifiers (deduction rule). (Contributed by NM, 4-Mar-1997.)
Hypothesis
Ref Expression
2ralbidva.1 ((φ (x A y B)) → (ψχ))
Assertion
Ref Expression
2ralbidva (φ → (x A y B ψx A y B χ))
Distinct variable groups:   x,y,φ   y,A
Allowed substitution hints:   ψ(x,y)   χ(x,y)   A(x)   B(x,y)

Proof of Theorem 2ralbidva
StepHypRef Expression
1 nfv 1619 . 2 xφ
2 nfv 1619 . 2 yφ
3 2ralbidva.1 . 2 ((φ (x A y B)) → (ψχ))
41, 2, 32ralbida 2653 1 (φ → (x A y B ψx A y B χ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358   wcel 1710  wral 2614
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-tru 1319  df-ex 1542  df-nf 1545  df-ral 2619
This theorem is referenced by: (None)
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