![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > simp322 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp322 | ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp22 1207 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant3 1135 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜏)) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1087 |
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 397 df-3an 1089 |
This theorem is referenced by: dalemqnet 38047 dalemrot 38052 dath2 38132 cdleme18d 38690 cdleme20i 38712 cdleme20j 38713 cdleme20l2 38716 cdleme20l 38717 cdleme20m 38718 cdleme20 38719 cdleme21j 38731 cdleme22eALTN 38740 cdleme26eALTN 38756 cdlemk16a 39251 cdlemk12u-2N 39285 cdlemk21-2N 39286 cdlemk22 39288 cdlemk31 39291 cdlemk32 39292 cdlemk11ta 39324 cdlemk11tc 39340 |
Copyright terms: Public domain | W3C validator |