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Mirrors > Home > MPE Home > Th. List > simp3r3 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3r3 | ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr3 1188 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒) | |
2 | 1 | 3ad2ant3 1127 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1079 |
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 208 df-an 397 df-3an 1081 |
This theorem is referenced by: nllyrest 22022 cdlemblem 36809 cdleme21 37353 cdleme22b 37357 cdleme40m 37483 cdlemg34 37728 cdlemk5u 37877 cdlemk6u 37878 cdlemk21N 37889 cdlemk20 37890 cdlemk26b-3 37921 cdlemk26-3 37922 cdlemk28-3 37924 cdlemky 37942 cdlemk11t 37962 cdlemkyyN 37978 dihmeetlem20N 38342 stoweidlem56 42218 |
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