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Mirrors > Home > MPE Home > Th. List > eeorOLD | Structured version Visualization version GIF version |
Description: Obsolete version of eeor 2330 as of 21-Nov-2024. (Contributed by NM, 8-Aug-1994.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eeor.1 | ⊢ Ⅎ𝑦𝜑 |
eeor.2 | ⊢ Ⅎ𝑥𝜓 |
Ref | Expression |
---|---|
eeorOLD | ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑦𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eeor.1 | . . . 4 ⊢ Ⅎ𝑦𝜑 | |
2 | 1 | 19.45 2232 | . . 3 ⊢ (∃𝑦(𝜑 ∨ 𝜓) ↔ (𝜑 ∨ ∃𝑦𝜓)) |
3 | 2 | exbii 1851 | . 2 ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜓) ↔ ∃𝑥(𝜑 ∨ ∃𝑦𝜓)) |
4 | eeor.2 | . . . 4 ⊢ Ⅎ𝑥𝜓 | |
5 | 4 | nfex 2318 | . . 3 ⊢ Ⅎ𝑥∃𝑦𝜓 |
6 | 5 | 19.44 2231 | . 2 ⊢ (∃𝑥(𝜑 ∨ ∃𝑦𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑦𝜓)) |
7 | 3, 6 | bitri 275 | 1 ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑦𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∨ wo 846 ∃wex 1782 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-10 2138 ax-11 2155 ax-12 2172 |
This theorem depends on definitions: df-bi 206 df-or 847 df-ex 1783 df-nf 1787 |
This theorem is referenced by: (None) |
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