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Theorem albi 1914
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 207 . . 3 ((𝜑𝜓) → (𝜑𝜓))
21al2imi 1911 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
3 biimpr 212 . . 3 ((𝜑𝜓) → (𝜓𝜑))
43al2imi 1911 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜓 → ∀𝑥𝜑))
52, 4impbid 204 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198  wal 1651
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905
This theorem depends on definitions:  df-bi 199
This theorem is referenced by:  albii  1915  nfbiit  1947  albidh  1964  19.16  2260  19.17  2261  equvel  2463  mobi  2592  mobiOLD  2593  eqeq1d  2801  intmin4  4696  dfiin2g  4743  eunex  5059  bj-2albi  33102  bj-hbxfrbi  33113  bj-eunex  33295  wl-aleq  33812  2albi  39359  ralbidar  39429  trsbcVD  39873  sbcssgVD  39879
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