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

Theorem rexlimd 2735
 Description: Deduction from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by NM, 27-May-1998.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Hypotheses
Ref Expression
rexlimd.1 xφ
rexlimd.2 xχ
rexlimd.3 (φ → (x A → (ψχ)))
Assertion
Ref Expression
rexlimd (φ → (x A ψχ))

Proof of Theorem rexlimd
StepHypRef Expression
1 rexlimd.1 . . 3 xφ
2 rexlimd.3 . . 3 (φ → (x A → (ψχ)))
31, 2ralrimi 2695 . 2 (φx A (ψχ))
4 rexlimd.2 . . 3 xχ
54r19.23 2729 . 2 (x A (ψχ) ↔ (x A ψχ))
63, 5sylib 188 1 (φ → (x A ψχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Ⅎwnf 1544   ∈ wcel 1710  ∀wral 2614  ∃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:  rexlimdv  2737  fun11iun  5305  ffnfv  5427
 Copyright terms: Public domain W3C validator