| Mathbox for Jonathan Ben-Naim |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj101 | 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 |
|---|---|
| bnj101.1 | ⊢ ∃𝑥𝜑 |
| bnj101.2 | ⊢ (𝜑 → 𝜓) |
| Ref | Expression |
|---|---|
| bnj101 | ⊢ ∃𝑥𝜓 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj101.1 | . 2 ⊢ ∃𝑥𝜑 | |
| 2 | bnj101.2 | . 2 ⊢ (𝜑 → 𝜓) | |
| 3 | 1, 2 | eximii 1837 | 1 ⊢ ∃𝑥𝜓 |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∃wex 1779 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 |
| This theorem depends on definitions: df-bi 207 df-ex 1780 |
| This theorem is referenced by: bnj1023 34794 bnj1098 34797 bnj1101 34798 bnj1109 34800 bnj1468 34860 bnj907 34981 bnj1110 34996 bnj1118 34998 bnj1128 35004 bnj1145 35007 bnj1172 35015 bnj1174 35017 bnj1176 35019 |
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