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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 2086 | . 2 ⊢ (∃𝑥𝜓 ↔ 𝜓) | |
3 | 1, 2 | sylib 210 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 |
This theorem depends on definitions: df-bi 199 df-ex 1881 |
This theorem is referenced by: bnj1265 31428 bnj1379 31446 bnj852 31536 bnj1148 31609 bnj1154 31612 bnj1189 31622 bnj1245 31627 bnj1286 31632 bnj1311 31637 bnj1371 31642 bnj1374 31644 bnj1498 31674 bnj1514 31676 |
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