![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > simp212 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp212 | ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp12 1201 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant2 1131 | 1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ 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: cdleme27a 37663 cdlemk5u 38157 cdlemk6u 38158 cdlemk7u 38166 cdlemk11u 38167 cdlemk12u 38168 cdlemk7u-2N 38184 cdlemk11u-2N 38185 cdlemk12u-2N 38186 cdlemk20-2N 38188 cdlemk22 38189 cdlemk22-3 38197 cdlemk33N 38205 cdlemk53b 38252 cdlemk53 38253 cdlemk55a 38255 cdlemkyyN 38258 cdlemk43N 38259 |
Copyright terms: Public domain | W3C validator |