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Mirrors > Home > MPE Home > Th. List > simp2l1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp2l1 | ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl1 1188 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑) | |
2 | 1 | 3ad2ant2 1131 | 1 ⊢ ((𝜏 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) ∧ 𝜂) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1084 |
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 206 df-an 396 df-3an 1086 |
This theorem is referenced by: poxp3 8133 btwnconn1lem8 35598 btwnconn1lem11 35601 btwnconn1lem12 35602 2lplnja 39002 cdlemk21-2N 40274 cdlemk19xlem 40325 jm2.27 42307 |
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