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Theorem hbanOLD 2228
Description: Obsolete proof of hban 2113 as of 6-Oct-2021. (Contributed by NM, 14-May-1993.) (Proof shortened by Wolf Lammen, 2-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
hbOLD.1 (𝜑 → ∀𝑥𝜑)
hbOLD.2 (𝜓 → ∀𝑥𝜓)
Assertion
Ref Expression
hbanOLD ((𝜑𝜓) → ∀𝑥(𝜑𝜓))

Proof of Theorem hbanOLD
StepHypRef Expression
1 hbOLD.1 . . . 4 (𝜑 → ∀𝑥𝜑)
21nfiOLD 1725 . . 3 𝑥𝜑
3 hbOLD.2 . . . 4 (𝜓 → ∀𝑥𝜓)
43nfiOLD 1725 . . 3 𝑥𝜓
52, 4nfanOLDOLD 2225 . 2 𝑥(𝜑𝜓)
65nfriOLD 2177 1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wal 1473
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nfOLD 1712
This theorem is referenced by: (None)
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