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Mirrors > Home > ILE Home > Th. List > hbia1 | GIF version |
Description: Lemma 23 of [Monk2] p. 114. (Contributed by NM, 29-May-2008.) |
Ref | Expression |
---|---|
hbia1 | ⊢ ((∀xφ → ∀xψ) → ∀x(∀xφ → ∀xψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hba1 1430 | . 2 ⊢ (∀xφ → ∀x∀xφ) | |
2 | hba1 1430 | . 2 ⊢ (∀xψ → ∀x∀xψ) | |
3 | 1, 2 | hbim 1434 | 1 ⊢ ((∀xφ → ∀xψ) → ∀x(∀xφ → ∀xψ)) |
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-5 1333 ax-gen 1335 ax-4 1397 ax-ial 1424 ax-i5r 1425 |
This theorem is referenced by: (None) |
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