New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rexlimdv3a GIF version

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-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-3an 936  df-ex 1542  df-nf 1545  df-ral 2619  df-rex 2620 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator