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Theorem albi 1736
 Description: Theorem 19.15 of [Margaris] p. 90. (Contributed by NM, 24-Jan-1993.)
Assertion
Ref Expression
albi (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))

Proof of Theorem albi
StepHypRef Expression
1 biimp 204 . . 3 ((𝜑𝜓) → (𝜑𝜓))
21al2imi 1733 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
3 biimpr 209 . . 3 ((𝜑𝜓) → (𝜓𝜑))
43al2imi 1733 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜓 → ∀𝑥𝜑))
52, 4impbid 201 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195  ∀wal 1473 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728 This theorem depends on definitions:  df-bi 196 This theorem is referenced by:  albii  1737  albidh  1780  19.16  2080  19.17  2081  equvel  2335  eqeq1d  2612  intmin4  4441  dfiin2g  4489  bj-2albi  31782  bj-hbxfrbi  31792  bj-nfbi  31793  bj-nfbiit  32024  wl-aleq  32501  2albi  37599  ralbidar  37670  sbcssOLD  37777  trsbcVD  38135  sbcssgVD  38141
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