Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
||
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 1979 | . 2 ⊢ (∃𝑥𝜓 ↔ 𝜓) | |
3 | 1, 2 | sylib 219 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 |
This theorem depends on definitions: df-bi 208 df-ex 1772 |
This theorem is referenced by: bnj1265 31983 bnj1379 32001 bnj852 32092 bnj1148 32165 bnj1154 32168 bnj1189 32178 bnj1245 32183 bnj1286 32188 bnj1311 32193 bnj1371 32198 bnj1374 32200 bnj1498 32230 bnj1514 32232 |
Copyright terms: Public domain | W3C validator |