![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > simp3l1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3l1 | ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl1 1188 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑) | |
2 | 1 | 3ad2ant3 1132 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ 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 210 df-an 400 df-3an 1086 |
This theorem is referenced by: cvmlift2lem10 32672 cdleme26ee 37656 cdleme36m 37757 cdleme40m 37763 cdlemg18b 37975 cdlemk5u 38157 cdlemk6u 38158 cdlemk21N 38169 cdlemk20 38170 cdlemk27-3 38203 cdlemk28-3 38204 dihmeetlem20N 38622 |
Copyright terms: Public domain | W3C validator |