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Theorem ralinexa 2659
 Description: A transformation of restricted quantifiers and logical connectives. (Contributed by NM, 4-Sep-2005.)
Assertion
Ref Expression
ralinexa (x A (φ → ¬ ψ) ↔ ¬ x A (φ ψ))

Proof of Theorem ralinexa
StepHypRef Expression
1 imnan 411 . . 3 ((φ → ¬ ψ) ↔ ¬ (φ ψ))
21ralbii 2638 . 2 (x A (φ → ¬ ψ) ↔ x A ¬ (φ ψ))
3 ralnex 2624 . 2 (x A ¬ (φ ψ) ↔ ¬ x A (φ ψ))
42, 3bitri 240 1 (x A (φ → ¬ ψ) ↔ ¬ x A (φ ψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∧ wa 358  ∀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-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-ral 2619  df-rex 2620 This theorem is referenced by: (None)
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