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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 1211 | . 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant3 1137 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1089 |
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 1091 |
This theorem is referenced by: ivthALT 34266 dalemclpjs 37390 dath2 37493 cdlema1N 37547 cdlemk7u 38626 cdlemk11u 38627 cdlemk12u 38628 cdlemk22 38649 cdlemk23-3 38658 cdlemk24-3 38659 cdlemk33N 38665 cdlemk11ta 38685 cdlemk11tc 38701 cdlemk54 38714 |
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