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| Mirrors > Home > MPE Home > Th. List > simpr3r | Structured version Visualization version GIF version | ||
| Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.) |
| Ref | Expression |
|---|---|
| simpr3r | ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simprr 773 | . 2 ⊢ ((𝜏 ∧ (𝜑 ∧ 𝜓)) → 𝜓) | |
| 2 | 1 | 3ad2antr3 1191 | 1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1087 |
| 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-3an 1089 |
| This theorem is referenced by: poxp2 8168 ax5seg 28953 segconeq 36011 ifscgr 36045 btwnconn1lem9 36096 btwnconn1lem11 36098 btwnconn1lem12 36099 lplnexllnN 39566 cdleme3b 40231 cdleme3c 40232 cdleme3e 40234 cdleme27a 40369 |
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