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Theorem r19.23 2729
 Description: Theorem 19.23 of [Margaris] p. 90 with restricted quantifiers. (Contributed by NM, 22-Oct-2010.) (Proof shortened by Mario Carneiro, 8-Oct-2016.)
Hypothesis
Ref Expression
r19.23.1 xψ
Assertion
Ref Expression
r19.23 (x A (φψ) ↔ (x A φψ))

Proof of Theorem r19.23
StepHypRef Expression
1 r19.23.1 . 2 xψ
2 r19.23t 2728 . 2 (Ⅎxψ → (x A (φψ) ↔ (x A φψ)))
31, 2ax-mp 5 1 (x A (φψ) ↔ (x A φψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  Ⅎwnf 1544  ∀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:  r19.23v  2730  rexlimi  2731  rexlimd  2735
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