![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 1059 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜒) | |
2 | 1 | 3ad2ant3 1077 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
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 196 df-an 385 df-3an 1033 |
This theorem is referenced by: cvmlift2lem10 30548 cdleme36m 34767 cdlemk5u 35167 cdlemk21N 35179 cdlemk20 35180 cdlemk27-3 35213 cdlemk28-3 35214 dihmeetlem20N 35633 |
Copyright terms: Public domain | W3C validator |