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Theorem hbim1 2303
Description: A closed form of hbim 2305. (Contributed by NM, 2-Jun-1993.)
Hypotheses
Ref Expression
hbim1.1 (𝜑 → ∀𝑥𝜑)
hbim1.2 (𝜑 → (𝜓 → ∀𝑥𝜓))
Assertion
Ref Expression
hbim1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))

Proof of Theorem hbim1
StepHypRef Expression
1 hbim1.2 . . 3 (𝜑 → (𝜓 → ∀𝑥𝜓))
21a2i 14 . 2 ((𝜑𝜓) → (𝜑 → ∀𝑥𝜓))
3 hbim1.1 . . 3 (𝜑 → ∀𝑥𝜑)
4319.21h 2293 . 2 (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓))
52, 4sylibr 237 1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2143  ax-12 2176
This theorem depends on definitions:  df-bi 210  df-ex 1782  df-nf 1786
This theorem is referenced by:  hbim  2305  axc14  2478
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