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Theorem albi 1820
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 214 . . 3 ((𝜑𝜓) → (𝜑𝜓))
21al2imi 1817 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
3 biimpr 219 . . 3 ((𝜑𝜓) → (𝜓𝜑))
43al2imi 1817 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜓 → ∀𝑥𝜑))
52, 4impbid 211 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wal 1539
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811
This theorem depends on definitions:  df-bi 206
This theorem is referenced by:  albii  1821  nfbiit  1853  albidh  1869  19.16  2218  19.17  2219  equvel  2454  eqeq1d  2738  raleqbidvv  3303  intmin4  4936  dfiin2g  4990  eunex  5343  bj-2albi  35010  bj-hbxfrbi  35026  bj-pm11.53vw  35173  bj-sblem  35242  wl-aleq  35926  2albi  42563  ralbidar  42630  trsbcVD  43064  sbcssgVD  43070  ichal  45553
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