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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj937 | Structured version Visualization version GIF version | ||
| Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| bnj937.1 | ⊢ (𝜑 → ∃𝑥𝜓) | 
| Ref | Expression | 
|---|---|
| bnj937 | ⊢ (𝜑 → 𝜓) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | bnj937.1 | . 2 ⊢ (𝜑 → ∃𝑥𝜓) | |
| 2 | 19.9v 1982 | . 2 ⊢ (∃𝑥𝜓 ↔ 𝜓) | |
| 3 | 1, 2 | sylib 218 | 1 ⊢ (𝜑 → 𝜓) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∃wex 1778 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 | 
| This theorem depends on definitions: df-bi 207 df-ex 1779 | 
| This theorem is referenced by: bnj1265 34827 bnj1379 34845 bnj852 34936 bnj1148 35011 bnj1154 35014 bnj1189 35024 bnj1245 35029 bnj1286 35034 bnj1311 35039 bnj1371 35044 bnj1374 35046 bnj1498 35076 bnj1514 35078 | 
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