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Mirrors > Home > MPE Home > Th. List > exlimdOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of exlimd 2074 as of 6-Oct-2021. (Contributed by NM, 23-Jan-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 12-Jan-2018.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
exlimdOLD.1 | ⊢ Ⅎ𝑥𝜑 |
exlimdOLD.2 | ⊢ Ⅎ𝑥𝜒 |
exlimdOLD.3 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
exlimdOLD | ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimdOLD.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | exlimdOLD.3 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 1, 2 | eximdOLD 2185 | . 2 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
4 | exlimdOLD.2 | . . 3 ⊢ Ⅎ𝑥𝜒 | |
5 | 4 | 19.9OLD 2193 | . 2 ⊢ (∃𝑥𝜒 ↔ 𝜒) |
6 | 3, 5 | syl6ib 240 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1695 ℲwnfOLD 1700 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nfOLD 1712 |
This theorem is referenced by: exlimdhOLD 2212 |
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