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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 1433 | . 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑) | |
2 | hba1 1433 | . 2 ⊢ (∀𝑥𝜓 → ∀𝑥∀𝑥𝜓) | |
3 | 1, 2 | hbim 1437 | 1 ⊢ ((∀𝑥𝜑 → ∀𝑥𝜓) → ∀𝑥(∀𝑥𝜑 → ∀𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1241 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-5 1336 ax-gen 1338 ax-4 1400 ax-ial 1427 ax-i5r 1428 |
This theorem is referenced by: (None) |
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