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Theorem hbim1 1503
Description: A closed form of hbim 1478. (Contributed by NM, 5-Aug-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 11 . 2 ((𝜑𝜓) → (𝜑 → ∀𝑥𝜓))
3 hbim1.1 . . 3 (𝜑 → ∀𝑥𝜑)
4319.21h 1490 . 2 (∀𝑥(𝜑𝜓) ↔ (𝜑 → ∀𝑥𝜓))
52, 4sylibr 132 1 ((𝜑𝜓) → ∀𝑥(𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  nfim1  1504  sbco2d  1882  sbco2vd  1883
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