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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 1559 | . 2 ⊢ (∃𝑥(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑥𝜓)) | |
2 | 19.44.1 | . . . 4 ⊢ Ⅎ𝑥𝜓 | |
3 | 2 | 19.9 1575 | . . 3 ⊢ (∃𝑥𝜓 ↔ 𝜓) |
4 | 3 | orbi2i 711 | . 2 ⊢ ((∃𝑥𝜑 ∨ ∃𝑥𝜓) ↔ (∃𝑥𝜑 ∨ 𝜓)) |
5 | 1, 4 | bitri 182 | 1 ⊢ (∃𝑥(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 103 ∨ wo 661 Ⅎwnf 1389 ∃wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-nf 1390 |
This theorem is referenced by: eeor 1625 |
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