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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 274 | 1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∃wex 1782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-11 2154 |
This theorem depends on definitions: df-bi 206 df-ex 1783 |
This theorem is referenced by: opabn0 5466 dmoprab 7376 rnoprab 7378 xpassen 8853 cnvoprabOLD 31055 elima4 33750 brimg 34239 ellines 34454 rnxrn 36524 fundcmpsurinj 44861 |
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