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Mirrors > Home > MPE Home > Th. List > simp3r2 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3r2 | ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr2 1192 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓) | |
2 | 1 | 3ad2ant3 1132 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ w3a 1084 |
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 210 df-an 400 df-3an 1086 |
This theorem is referenced by: nllyrest 22091 cdlemblem 37089 cdleme21 37633 cdleme22b 37637 cdleme40m 37763 cdlemg34 38008 cdlemk5u 38157 cdlemk6u 38158 cdlemk21N 38169 cdlemk20 38170 cdlemk26b-3 38201 cdlemk26-3 38202 cdlemk28-3 38204 cdlemky 38222 cdlemk11t 38242 cdlemkyyN 38258 stoweidlem56 42698 |
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