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Theorem rexlimddv 2742
 Description: Restricted existential elimination rule of natural deduction. (Contributed by Mario Carneiro, 15-Jun-2016.)
Hypotheses
Ref Expression
rexlimddv.1 (φx A ψ)
rexlimddv.2 ((φ (x A ψ)) → χ)
Assertion
Ref Expression
rexlimddv (φχ)
Distinct variable groups:   φ,x   χ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem rexlimddv
StepHypRef Expression
1 rexlimddv.1 . 2 (φx A ψ)
2 rexlimddv.2 . . 3 ((φ (x A ψ)) → χ)
32rexlimdvaa 2739 . 2 (φ → (x A ψχ))
41, 3mpd 14 1 (φχ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∈ wcel 1710  ∃wrex 2615 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  df-ral 2619  df-rex 2620 This theorem is referenced by: (None)
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