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Mirrors > Home > ILE 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 1682 | . . 3 ⊢ (∃𝑦∃𝑧∃𝑤𝜑 ↔ ∃𝑤∃𝑧∃𝑦𝜑) | |
2 | 1 | exbii 1598 | . 2 ⊢ (∃𝑥∃𝑦∃𝑧∃𝑤𝜑 ↔ ∃𝑥∃𝑤∃𝑧∃𝑦𝜑) |
3 | excom13 1682 | . 2 ⊢ (∃𝑥∃𝑤∃𝑧∃𝑦𝜑 ↔ ∃𝑧∃𝑤∃𝑥∃𝑦𝜑) | |
4 | 2, 3 | bitri 183 | 1 ⊢ (∃𝑥∃𝑦∃𝑧∃𝑤𝜑 ↔ ∃𝑧∃𝑤∃𝑥∃𝑦𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∃wex 1485 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: ee8anv 1928 elvvv 4674 dfoprab2 5900 xpassen 6808 enq0sym 7394 |
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