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Mirrors > Home > MPE Home > Th. List > simp332 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp332 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp32 1206 | . 2 ⊢ ((𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ 𝜏 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
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 33678 dalemclqjt 36765 dath2 36867 cdlema1N 36921 cdleme26eALTN 37491 cdlemk7u 38000 cdlemk11u 38001 cdlemk12u 38002 cdlemk23-3 38032 cdlemk33N 38039 cdlemk11ta 38059 cdlemk11tc 38075 cdlemk54 38088 |
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