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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1196 | 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 |
---|---|
bnj1196.1 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
Ref | Expression |
---|---|
bnj1196 | ⊢ (𝜑 → ∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1196.1 | . 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) | |
2 | df-rex 3147 | . 2 ⊢ (∃𝑥 ∈ 𝐴 𝜓 ↔ ∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜓)) | |
3 | 1, 2 | sylib 220 | 1 ⊢ (𝜑 → ∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 ∃wex 1779 ∈ wcel 2113 ∃wrex 3142 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 209 df-rex 3147 |
This theorem is referenced by: bnj1209 32072 bnj1265 32088 bnj1379 32106 bnj1521 32127 bnj900 32205 bnj986 32231 bnj1189 32285 bnj1245 32290 bnj1286 32295 bnj1311 32300 bnj1450 32326 bnj1498 32337 |
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