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Mirrors > Home > MPE Home > Th. List > simp1r1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp1r1 | ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr1 1195 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant1 1134 | 1 ⊢ (((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜏 ∧ 𝜂) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∧ w3a 1088 |
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 1090 |
This theorem is referenced by: trisegint 33960 lshpkrlem6 36741 atbtwnexOLDN 37073 atbtwnex 37074 3dim3 37095 3atlem5 37113 4atlem11 37235 4atexlem7 37701 cdleme22b 37967 |
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