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Theorem rexlimi 2731
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 30-Nov-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.)
Hypotheses
Ref Expression
rexlimi.1 xψ
rexlimi.2 (x A → (φψ))
Assertion
Ref Expression
rexlimi (x A φψ)

Proof of Theorem rexlimi
StepHypRef Expression
1 rexlimi.2 . . 3 (x A → (φψ))
21rgen 2679 . 2 x A (φψ)
3 rexlimi.1 . . 3 xψ
43r19.23 2729 . 2 (x A (φψ) ↔ (x A φψ))
52, 4mpbi 199 1 (x A φψ)
 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:  rexlimiv  2732  fun11iun  5305
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