Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > excom13 | GIF version |
Description: Swap 1st and 3rd existential quantifiers. (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
excom13 | ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1651 | . 2 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑦∃𝑥∃𝑧𝜑) | |
2 | excom 1651 | . . 3 ⊢ (∃𝑥∃𝑧𝜑 ↔ ∃𝑧∃𝑥𝜑) | |
3 | 2 | exbii 1592 | . 2 ⊢ (∃𝑦∃𝑥∃𝑧𝜑 ↔ ∃𝑦∃𝑧∃𝑥𝜑) |
4 | excom 1651 | . 2 ⊢ (∃𝑦∃𝑧∃𝑥𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑) | |
5 | 1, 3, 4 | 3bitri 205 | 1 ⊢ (∃𝑥∃𝑦∃𝑧𝜑 ↔ ∃𝑧∃𝑦∃𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∃wex 1479 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: exrot3 1677 exrot4 1678 euotd 4226 |
Copyright terms: Public domain | W3C validator |