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Mathbox for Jonathan Ben-Naim |
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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 1987 | . 2 ⊢ (∃𝑥𝜓 ↔ 𝜓) | |
3 | 1, 2 | sylib 217 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1781 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 |
This theorem depends on definitions: df-bi 206 df-ex 1782 |
This theorem is referenced by: bnj1265 33554 bnj1379 33572 bnj852 33663 bnj1148 33738 bnj1154 33741 bnj1189 33751 bnj1245 33756 bnj1286 33761 bnj1311 33766 bnj1371 33771 bnj1374 33773 bnj1498 33803 bnj1514 33805 |
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