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Mirrors > Home > ILE Home > Th. List > hbim1 | GIF version |
Description: A closed form of hbim 1434. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
hbim1.1 | ⊢ (φ → ∀xφ) |
hbim1.2 | ⊢ (φ → (ψ → ∀xψ)) |
Ref | Expression |
---|---|
hbim1 | ⊢ ((φ → ψ) → ∀x(φ → ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbim1.2 | . . 3 ⊢ (φ → (ψ → ∀xψ)) | |
2 | 1 | a2i 11 | . 2 ⊢ ((φ → ψ) → (φ → ∀xψ)) |
3 | hbim1.1 | . . 3 ⊢ (φ → ∀xφ) | |
4 | 3 | 19.21h 1446 | . 2 ⊢ (∀x(φ → ψ) ↔ (φ → ∀xψ)) |
5 | 2, 4 | sylibr 137 | 1 ⊢ ((φ → ψ) → ∀x(φ → ψ)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1240 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-4 1397 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: nfim1 1460 sbco2d 1837 sbco2vd 1838 |
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