Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > simp3r1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3r1 | ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr1 1190 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 ∧ w3a 1083 |
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 209 df-an 399 df-3an 1085 |
This theorem is referenced by: nllyrest 22088 segletr 33570 cdlemblem 36923 cdleme21 37467 cdleme22b 37471 cdleme40m 37597 cdlemg34 37842 cdlemk5u 37991 cdlemk6u 37992 cdlemk21N 38003 cdlemk20 38004 cdlemk26b-3 38035 cdlemk26-3 38036 cdlemk28-3 38038 cdlemk37 38044 cdlemky 38056 cdlemk11t 38076 cdlemkyyN 38092 dihmeetlem20N 38456 stoweidlem56 42334 |
Copyright terms: Public domain | W3C validator |