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| Mirrors > Home > MPE Home > Th. List > simpr1 | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) |
| Ref | Expression |
|---|---|
| simpr1 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpr 484 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
| 2 | 1 | 3ad2antr1 1189 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜓) |
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