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Mirrors > Home > MPE Home > Th. List > simp221 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp221 | ⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜁) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp21 1208 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant2 1136 | 1 ⊢ ((𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) ∧ 𝜁) → 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: 4atexlemcnd 37823 cdleme26eALTN 38112 cdleme27a 38118 cdlemk23-3 38653 cdlemk25-3 38655 cdlemk27-3 38658 |
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