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Mirrors > Home > MPE Home > Th. List > simp3l1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3l1 | ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl1 1187 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜑) | |
2 | 1 | 3ad2ant3 1131 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 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: cvmlift2lem10 32561 cdleme26ee 37498 cdleme36m 37599 cdleme40m 37605 cdlemg18b 37817 cdlemk5u 37999 cdlemk6u 38000 cdlemk21N 38011 cdlemk20 38012 cdlemk27-3 38045 cdlemk28-3 38046 dihmeetlem20N 38464 |
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