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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 3146 | . 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 1780 ∈ wcel 2114 ∃wrex 3141 |
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 3146 |
This theorem is referenced by: bnj1209 32070 bnj1265 32086 bnj1379 32104 bnj1521 32125 bnj900 32203 bnj986 32229 bnj1189 32283 bnj1245 32288 bnj1286 32293 bnj1311 32298 bnj1450 32324 bnj1498 32335 |
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