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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 1191 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant3 1132 | 1 ⊢ ((𝜏 ∧ 𝜂 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 ∧ w3a 1084 |
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 395 df-3an 1086 |
This theorem is referenced by: nllyrest 23481 segletr 35938 cdlemblem 39492 cdleme21 40036 cdleme22b 40040 cdleme40m 40166 cdlemg34 40411 cdlemk5u 40560 cdlemk6u 40561 cdlemk21N 40572 cdlemk20 40573 cdlemk26b-3 40604 cdlemk26-3 40605 cdlemk28-3 40607 cdlemk37 40613 cdlemky 40625 cdlemk11t 40645 cdlemkyyN 40661 dihmeetlem20N 41025 stoweidlem56 45677 |
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