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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1219 | 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 |
---|---|
bnj1219.1 | ⊢ (𝜒 ↔ (𝜑 ∧ 𝜓 ∧ 𝜁)) |
bnj1219.2 | ⊢ (𝜃 ↔ (𝜒 ∧ 𝜏 ∧ 𝜂)) |
Ref | Expression |
---|---|
bnj1219 | ⊢ (𝜃 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1219.2 | . 2 ⊢ (𝜃 ↔ (𝜒 ∧ 𝜏 ∧ 𝜂)) | |
2 | bnj1219.1 | . . 3 ⊢ (𝜒 ↔ (𝜑 ∧ 𝜓 ∧ 𝜁)) | |
3 | 2 | simp2bi 1145 | . 2 ⊢ (𝜒 → 𝜓) |
4 | 1, 3 | bnj835 32725 | 1 ⊢ (𝜃 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∧ w3a 1086 |
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 206 df-an 397 df-3an 1088 |
This theorem is referenced by: bnj1379 32796 |
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