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| Mirrors > Home > MPE Home > Th. List > exrot3 | Structured version Visualization version 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 2164 | . 2 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑) | |
| 2 | excom 2162 | . 2 ⊢ (∃𝑧∃𝑦∃𝑥𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑) | |
| 3 | 1, 2 | bitri 275 | 1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ↔ wb 206 ∃wex 1779 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-11 2157 | 
| This theorem depends on definitions: df-bi 207 df-ex 1780 | 
| This theorem is referenced by: opabn0 5558 dmoprab 7536 rnoprab 7538 xpassen 9106 elima4 35776 brimg 35938 ellines 36153 rnxrn 38399 fundcmpsurinj 47396 | 
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