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Mirrors > Home > ILE Home > Th. List > alcoms | GIF version |
Description: Swap quantifiers in an antecedent. (Contributed by NM, 11-May-1993.) |
Ref | Expression |
---|---|
alcoms.1 | ⊢ (∀𝑥∀𝑦𝜑 → 𝜓) |
Ref | Expression |
---|---|
alcoms | ⊢ (∀𝑦∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-7 1428 | . 2 ⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦𝜑) | |
2 | alcoms.1 | . 2 ⊢ (∀𝑥∀𝑦𝜑 → 𝜓) | |
3 | 1, 2 | syl 14 | 1 ⊢ (∀𝑦∀𝑥𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1333 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-7 1428 |
This theorem is referenced by: bj-nfalt 13409 |
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