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Mirrors > Home > MPE Home > Th. List > exanOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of exan 1853 as of 19-Jun-2023. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) Reduce axiom dependencies. (Revised by BJ, 7-Jul-2021.) (Proof shortened by Wolf Lammen, 6-Nov-2022.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
exanOLD.1 | ⊢ (∃𝑥𝜑 ∧ 𝜓) |
Ref | Expression |
---|---|
exanOLD | ⊢ ∃𝑥(𝜑 ∧ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exanOLD.1 | . . 3 ⊢ (∃𝑥𝜑 ∧ 𝜓) | |
2 | 1 | simpli 484 | . 2 ⊢ ∃𝑥𝜑 |
3 | 1 | simpri 486 | . . 3 ⊢ 𝜓 |
4 | 3 | jctr 525 | . 2 ⊢ (𝜑 → (𝜑 ∧ 𝜓)) |
5 | 2, 4 | eximii 1828 | 1 ⊢ ∃𝑥(𝜑 ∧ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 396 ∃wex 1771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 |
This theorem is referenced by: (None) |
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