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Mirrors > Home > MPE Home > Th. List > simp3r3 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3r3 | ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr3 1195 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒) | |
2 | 1 | 3ad2ant3 1134 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1086 |
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 1088 |
This theorem is referenced by: nllyrest 22637 cdlemblem 37807 cdleme21 38351 cdleme22b 38355 cdleme40m 38481 cdlemg34 38726 cdlemk5u 38875 cdlemk6u 38876 cdlemk21N 38887 cdlemk20 38888 cdlemk26b-3 38919 cdlemk26-3 38920 cdlemk28-3 38922 cdlemky 38940 cdlemk11t 38960 cdlemkyyN 38976 dihmeetlem20N 39340 stoweidlem56 43597 |
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