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Mirrors > Home > ILE Home > Th. List > exrot3 | GIF version |
Description: Rotate existential quantifiers. (Contributed by NM, 17-Mar-1995.) |
Ref | Expression |
---|---|
exrot3 | ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom13 1689 | . 2 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑) | |
2 | excom 1664 | . 2 ⊢ (∃𝑧∃𝑦∃𝑥𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑) | |
3 | 1, 2 | bitri 184 | 1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 105 ∃wex 1492 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: opabm 4280 rexiunxp 4769 dmoprab 5955 rnoprab 5957 cnvoprab 6234 xpassen 6829 dmaddpq 7377 dmmulpq 7378 |
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