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Mirrors > Home > MPE Home > Th. List > simp331 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp331 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp31 1097 | . 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant3 1084 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1037 |
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 197 df-an 386 df-3an 1039 |
This theorem is referenced by: ivthALT 32330 dalemclpjs 34920 dath2 35023 cdlema1N 35077 cdlemk7u 36158 cdlemk11u 36159 cdlemk12u 36160 cdlemk22 36181 cdlemk23-3 36190 cdlemk24-3 36191 cdlemk33N 36197 cdlemk11ta 36217 cdlemk11tc 36233 cdlemk54 36246 |
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