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Mirrors > Home > MPE Home > Th. List > exrot4 | Structured version Visualization version 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 2170 | . . 3 ⊢ (∃𝑦∃𝑧∃𝑤𝜑 ↔ ∃𝑤∃𝑧∃𝑦𝜑) | |
2 | 1 | exbii 1847 | . 2 ⊢ (∃𝑥∃𝑦∃𝑧∃𝑤𝜑 ↔ ∃𝑥∃𝑤∃𝑧∃𝑦𝜑) |
3 | excom13 2170 | . 2 ⊢ (∃𝑥∃𝑤∃𝑧∃𝑦𝜑 ↔ ∃𝑧∃𝑤∃𝑥∃𝑦𝜑) | |
4 | 2, 3 | bitri 277 | 1 ⊢ (∃𝑥∃𝑦∃𝑧∃𝑤𝜑 ↔ ∃𝑧∃𝑤∃𝑥∃𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∃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 2160 |
This theorem depends on definitions: df-bi 209 df-ex 1780 |
This theorem is referenced by: elvvv 5630 dfoprab2 7215 xpassen 8614 5oalem7 29440 elfuns 33380 fundcmpsurbijinj 43577 |
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