| Mathbox for Jonathan Ben-Naim |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1254 | 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 |
|---|---|
| bnj1254.1 | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏)) |
| Ref | Expression |
|---|---|
| bnj1254 | ⊢ (𝜑 → 𝜏) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj1254.1 | . 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏)) | |
| 2 | id 22 | . . 3 ⊢ (𝜏 → 𝜏) | |
| 3 | 2 | bnj708 34770 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜏) |
| 4 | 1, 3 | sylbi 217 | 1 ⊢ (𝜑 → 𝜏) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ↔ wb 206 ∧ w-bnj17 34700 |
| 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 207 df-an 396 df-bnj17 34701 |
| This theorem is referenced by: bnj554 34913 bnj557 34915 bnj967 34959 bnj999 34972 bnj907 34981 bnj1118 34998 bnj1128 35004 bnj1253 35031 bnj1450 35064 |
| Copyright terms: Public domain | W3C validator |