Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > excomim | GIF version |
Description: One direction of Theorem 19.11 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
excomim | ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a 1482 | . . 3 ⊢ (𝜑 → ∃𝑥𝜑) | |
2 | 1 | 2eximi 1492 | . 2 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦∃𝑥𝜑) |
3 | hbe1 1384 | . . . 4 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑) | |
4 | 3 | hbex 1527 | . . 3 ⊢ (∃𝑦∃𝑥𝜑 → ∀𝑥∃𝑦∃𝑥𝜑) |
5 | 4 | 19.9h 1534 | . 2 ⊢ (∃𝑥∃𝑦∃𝑥𝜑 ↔ ∃𝑦∃𝑥𝜑) |
6 | 2, 5 | sylib 127 | 1 ⊢ (∃𝑥∃𝑦𝜑 → ∃𝑦∃𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: excom 1554 2euswapdc 1991 |
Copyright terms: Public domain | W3C validator |