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Mirrors > Home > NFE Home > Th. List > alrot3 | GIF version |
Description: Theorem *11.21 in [WhiteheadRussell] p. 160. (Contributed by Andrew Salmon, 24-May-2011.) |
Ref | Expression |
---|---|
alrot3 | ⊢ (∀x∀y∀zφ ↔ ∀y∀z∀xφ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 1737 | . 2 ⊢ (∀x∀y∀zφ ↔ ∀y∀x∀zφ) | |
2 | alcom 1737 | . . 3 ⊢ (∀x∀zφ ↔ ∀z∀xφ) | |
3 | 2 | albii 1566 | . 2 ⊢ (∀y∀x∀zφ ↔ ∀y∀z∀xφ) |
4 | 1, 3 | bitri 240 | 1 ⊢ (∀x∀y∀zφ ↔ ∀y∀z∀xφ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-7 1734 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: alrot4 1739 ssrelk 4211 eqrelk 4212 sikexlem 4295 insklem 4304 raliunxp 4823 ssopr 4846 dffun2 5119 fun11 5159 |
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