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Mirrors > Home > MPE Home > Th. List > simp311 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp311 | ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp11 1204 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant3 1136 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1088 |
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 1090 |
This theorem is referenced by: dalem-clpjq 37274 dath2 37374 cdleme26e 37996 cdleme38m 38100 cdleme38n 38101 cdleme39n 38103 cdlemg28b 38340 cdlemk7 38485 cdlemk11 38486 cdlemk12 38487 cdlemk7u 38507 cdlemk11u 38508 cdlemk12u 38509 cdlemk22 38530 cdlemk23-3 38539 cdlemk25-3 38541 |
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