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Theorem albi 1427
Description: Theorem 19.15 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
albi (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))

Proof of Theorem albi
StepHypRef Expression
1 bi1 117 . . 3 ((𝜑𝜓) → (𝜑𝜓))
21al2imi 1417 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
3 bi2 129 . . 3 ((𝜑𝜓) → (𝜓𝜑))
43al2imi 1417 . 2 (∀𝑥(𝜑𝜓) → (∀𝑥𝜓 → ∀𝑥𝜑))
52, 4impbid 128 1 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 ↔ ∀𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  wal 1312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  albii  1429  albidh  1439  19.16  1517  19.17  1518  intmin4  3767  dfiin2g  3814
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