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Theorem hbng 30761
Description: A more general form of hbn 2129. (Contributed by Scott Fenton, 13-Dec-2010.)
Hypothesis
Ref Expression
hbg.1 (𝜑 → ∀𝑥𝜓)
Assertion
Ref Expression
hbng 𝜓 → ∀𝑥 ¬ 𝜑)

Proof of Theorem hbng
StepHypRef Expression
1 hbntg 30758 . 2 (∀𝑥(𝜑 → ∀𝑥𝜓) → (¬ 𝜓 → ∀𝑥 ¬ 𝜑))
2 hbg.1 . 2 (𝜑 → ∀𝑥𝜓)
31, 2mpg 1714 1 𝜓 → ∀𝑥 ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-12 2032
This theorem depends on definitions:  df-bi 195  df-ex 1695
This theorem is referenced by: (None)
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