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Mirrors > Home > MPE Home > Th. List > simp3l3 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3l3 | ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl3 1203 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) | |
2 | 1 | 3ad2ant3 1126 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 386 ∧ w3a 1071 |
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 387 df-3an 1073 |
This theorem is referenced by: cvmlift2lem10 31893 cdleme36m 36615 cdlemk5u 37015 cdlemk21N 37027 cdlemk20 37028 cdlemk27-3 37061 cdlemk28-3 37062 dihmeetlem20N 37480 |
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