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Mirrors > Home > NFE Home > Th. List > exrot4 | GIF version |
Description: Rotate existential quantifiers twice. (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
exrot4 | ⊢ (∃x∃y∃z∃wφ ↔ ∃z∃w∃x∃yφ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom13 1743 | . . 3 ⊢ (∃y∃z∃wφ ↔ ∃w∃z∃yφ) | |
2 | 1 | exbii 1582 | . 2 ⊢ (∃x∃y∃z∃wφ ↔ ∃x∃w∃z∃yφ) |
3 | excom13 1743 | . 2 ⊢ (∃x∃w∃z∃yφ ↔ ∃z∃w∃x∃yφ) | |
4 | 2, 3 | bitri 240 | 1 ⊢ (∃x∃y∃z∃wφ ↔ ∃z∃w∃x∃yφ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ∃wex 1541 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-7 1734 |
This theorem depends on definitions: df-bi 177 df-ex 1542 |
This theorem is referenced by: sikexlem 4295 insklem 4304 elswap 4740 dfoprab2 5558 brpprod 5839 lecex 6115 |
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