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Theorem aaanOLD 2333
Description: Obsolete version of aaan 2332 as of 21-Nov-2024. (Contributed by NM, 12-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
aaan.1 𝑦𝜑
aaan.2 𝑥𝜓
Assertion
Ref Expression
aaanOLD (∀𝑥𝑦(𝜑𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑦𝜓))

Proof of Theorem aaanOLD
StepHypRef Expression
1 aaan.1 . . . 4 𝑦𝜑
2119.28 2226 . . 3 (∀𝑦(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑦𝜓))
32albii 1816 . 2 (∀𝑥𝑦(𝜑𝜓) ↔ ∀𝑥(𝜑 ∧ ∀𝑦𝜓))
4 aaan.2 . . . 4 𝑥𝜓
54nfal 2322 . . 3 𝑥𝑦𝜓
6519.27 2225 . 2 (∀𝑥(𝜑 ∧ ∀𝑦𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑦𝜓))
73, 6bitri 275 1 (∀𝑥𝑦(𝜑𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑦𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wa 395  wal 1535  wnf 1780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-11 2155  ax-12 2175
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-nf 1781
This theorem is referenced by: (None)
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