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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 1174 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant3 1115 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 387 ∧ w3a 1068 |
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 388 df-3an 1070 |
This theorem is referenced by: nllyrest 21788 segletr 33036 cdlemblem 36322 cdleme21 36866 cdleme22b 36870 cdleme40m 36996 cdlemg34 37241 cdlemk5u 37390 cdlemk6u 37391 cdlemk21N 37402 cdlemk20 37403 cdlemk26b-3 37434 cdlemk26-3 37435 cdlemk28-3 37437 cdlemk37 37443 cdlemky 37455 cdlemk11t 37475 cdlemkyyN 37491 dihmeetlem20N 37855 stoweidlem56 41718 |
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