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Mirrors > Home > MPE Home > Th. List > alcoms | Structured version Visualization version 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-11 2160 | . 2 ⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦𝜑) | |
2 | alcoms.1 | . 2 ⊢ (∀𝑥∀𝑦𝜑 → 𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (∀𝑦∀𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1534 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-11 2160 |
This theorem is referenced by: cbv2h 2425 mo3 2647 bj-nfalt 34049 bj-cbv3ta 34112 bj-cbv2hv 34123 wl-equsal1i 34787 wl-mo3t 34816 axc11n-16 36078 axc11next 40744 |
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