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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 1207 | . 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1083 |
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 209 df-an 399 df-3an 1085 |
This theorem is referenced by: ivthALT 33685 dalemclrju 36774 dath2 36875 cdlema1N 36929 cdleme26eALTN 37499 cdlemk7u 38008 cdlemk11u 38009 cdlemk12u 38010 cdlemk22 38031 cdlemk23-3 38040 cdlemk33N 38047 cdlemk11ta 38067 cdlemk11tc 38083 cdlemk54 38096 |
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