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Mirrors > Home > MPE Home > Th. List > simp2r1 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp2r1 | ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr1 1193 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜑) | |
2 | 1 | 3ad2ant2 1133 | 1 ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜑) |
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: btwnconn1lem8 34396 btwnconn1lem9 34397 btwnconn1lem10 34398 btwnconn1lem11 34399 btwnconn1lem12 34400 jm2.27 40830 |
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