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

Theorem reximdv 2725
 Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Restricted quantifier version with strong hypothesis.) (Contributed by NM, 24-Jun-1998.)
Hypothesis
Ref Expression
reximdv.1 (φ → (ψχ))
Assertion
Ref Expression
reximdv (φ → (x A ψx A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem reximdv
StepHypRef Expression
1 reximdv.1 . . 3 (φ → (ψχ))
21a1d 22 . 2 (φ → (x A → (ψχ)))
32reximdvai 2724 1 (φ → (x A ψx A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ 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-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:  r19.12  2727  fvelima  5369
 Copyright terms: Public domain W3C validator