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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 2021 | . 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 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-11 2021 |
This theorem is referenced by: cbv3hvOLDOLD 2162 cbv2h 2257 mo3 2495 bj-nfalt 31889 bj-cbv3ta 31897 bj-cbv2hv 31918 bj-mo3OLD 32022 wl-equsal1i 32508 wl-mo3t 32537 axc11n-16 33241 axc11next 37629 |
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