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Mirrors > Home > MPE Home > Th. List > simp3r2 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3r2 | ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr2 1197 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜓) | |
2 | 1 | 3ad2ant3 1137 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ w3a 1089 |
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 210 df-an 400 df-3an 1091 |
This theorem is referenced by: nllyrest 22407 cdlemblem 37571 cdleme21 38115 cdleme22b 38119 cdleme40m 38245 cdlemg34 38490 cdlemk5u 38639 cdlemk6u 38640 cdlemk21N 38651 cdlemk20 38652 cdlemk26b-3 38683 cdlemk26-3 38684 cdlemk28-3 38686 cdlemky 38704 cdlemk11t 38724 cdlemkyyN 38740 stoweidlem56 43301 |
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