Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 19.44 | GIF version |
Description: Theorem 19.44 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.) |
Ref | Expression |
---|---|
19.44.1 | ⊢ Ⅎ𝑥𝜓 |
Ref | Expression |
---|---|
19.44 | ⊢ (∃𝑥(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.43 1519 | . 2 ⊢ (∃𝑥(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑥𝜓)) | |
2 | 19.44.1 | . . . 4 ⊢ Ⅎ𝑥𝜓 | |
3 | 2 | 19.9 1535 | . . 3 ⊢ (∃𝑥𝜓 ↔ 𝜓) |
4 | 3 | orbi2i 679 | . 2 ⊢ ((∃𝑥𝜑 ∨ ∃𝑥𝜓) ↔ (∃𝑥𝜑 ∨ 𝜓)) |
5 | 1, 4 | bitri 173 | 1 ⊢ (∃𝑥(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 ∨ wo 629 Ⅎwnf 1349 ∃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-io 630 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: eeor 1585 |
Copyright terms: Public domain | W3C validator |