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Theorem rexlimdv3a 2740
Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv 2737. (Contributed by NM, 7-Jun-2015.)
Hypothesis
Ref Expression
rexlimdv3a.1 ((φ x A ψ) → χ)
Assertion
Ref Expression
rexlimdv3a (φ → (x A ψχ))
Distinct variable groups:   φ,x   χ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem rexlimdv3a
StepHypRef Expression
1 rexlimdv3a.1 . . 3 ((φ x A ψ) → χ)
213exp 1150 . 2 (φ → (x A → (ψχ)))
32rexlimdv 2737 1 (φ → (x A ψχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   w3a 934   wcel 1710  wrex 2615
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-6 1729  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  df-rex 2620
This theorem is referenced by: (None)
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