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Theorem albi 1734
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 203 . . 3 ((𝜑𝜓) → (𝜑𝜓))
21al2imi 1731 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
3 biimpr 208 . . 3 ((𝜑𝜓) → (𝜓𝜑))
43al2imi 1731 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜓 → ∀𝑥𝜑))
52, 4impbid 200 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726
This theorem depends on definitions:  df-bi 195
This theorem is referenced by:  albii  1735  albidh  1778  19.16  2077  19.17  2078  equvel  2330  eqeq1d  2607  intmin4  4431  dfiin2g  4479  bj-2albi  31584  bj-hbxfrbi  31594  bj-nfbi  31595  wl-aleq  32300  2albi  37398  ralbidar  37469  sbcssOLD  37576  trsbcVD  37934  sbcssgVD  37940
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