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Theorem albi 1744
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 205 . . 3 ((𝜑𝜓) → (𝜑𝜓))
21al2imi 1741 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
3 biimpr 210 . . 3 ((𝜑𝜓) → (𝜓𝜑))
43al2imi 1741 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜓 → ∀𝑥𝜑))
52, 4impbid 202 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1479
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735
This theorem depends on definitions:  df-bi 197
This theorem is referenced by:  albii  1745  nfbiit  1775  albidh  1791  19.16  2091  19.17  2092  equvel  2345  eqeq1d  2622  intmin4  4497  dfiin2g  4544  bj-2albi  32572  bj-hbxfrbi  32583  wl-aleq  33293  2albi  38397  ralbidar  38469  sbcssOLD  38576  trsbcVD  38933  sbcssgVD  38939
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