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Mirrors > Home > MPE Home > Th. List > simp333 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp333 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp33 1269 | . 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒) | |
2 | 1 | 3ad2ant3 1166 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1108 |
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 199 df-an 386 df-3an 1110 |
This theorem is referenced by: ivthALT 32842 dalemclrju 35657 dath2 35758 cdlema1N 35812 cdleme26eALTN 36382 cdlemk7u 36891 cdlemk11u 36892 cdlemk12u 36893 cdlemk22 36914 cdlemk23-3 36923 cdlemk33N 36930 cdlemk11ta 36950 cdlemk11tc 36966 cdlemk54 36979 |
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