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Mirrors > Home > MPE Home > Th. List > simp312 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp312 | ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp12 1200 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜓) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜂 ∧ 𝜁 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏)) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ 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: dalemrot 36808 dalem-cly 36822 dath2 36888 cdleme26e 37510 cdleme38m 37614 cdleme38n 37615 cdleme39n 37617 cdlemg28b 37854 cdlemk7 37999 cdlemk11 38000 cdlemk12 38001 cdlemk7u 38021 cdlemk11u 38022 cdlemk12u 38023 cdlemk22 38044 cdlemk23-3 38053 cdlemk25-3 38055 |
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