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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 1189 | 1 ⊢ ((𝜏 ∧ (𝜒 ∧ 𝜃 ∧ (𝜑 ∧ 𝜓))) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ 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 207 df-an 396 df-3an 1088 |
This theorem is referenced by: poxp2 8167 ax5seg 28968 segconeq 35992 ifscgr 36026 btwnconn1lem9 36077 btwnconn1lem11 36079 btwnconn1lem12 36080 lplnexllnN 39547 cdleme3b 40212 cdleme3c 40213 cdleme3e 40215 cdleme27a 40350 |
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