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Mirrors > Home > MPE Home > Th. List > simp3l2 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3l2 | ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl2 1248 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓) | |
2 | 1 | 3ad2ant3 1169 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 386 ∧ w3a 1111 |
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 199 df-an 387 df-3an 1113 |
This theorem is referenced by: cvmlift2lem10 31836 cdleme36m 36531 cdlemk5u 36931 cdlemk6u 36932 cdlemk21N 36943 cdlemk20 36944 cdlemk27-3 36977 cdlemk28-3 36978 |
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