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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 1194 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant3 1135 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1087 |
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 206 df-an 397 df-3an 1089 |
This theorem is referenced by: nllyrest 22821 segletr 34666 cdlemblem 38223 cdleme21 38767 cdleme22b 38771 cdleme40m 38897 cdlemg34 39142 cdlemk5u 39291 cdlemk6u 39292 cdlemk21N 39303 cdlemk20 39304 cdlemk26b-3 39335 cdlemk26-3 39336 cdlemk28-3 39338 cdlemk37 39344 cdlemky 39356 cdlemk11t 39376 cdlemkyyN 39392 dihmeetlem20N 39756 stoweidlem56 44229 |
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