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Mirrors > Home > MPE Home > Th. List > simp2r3 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp2r3 | ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr3 1256 | . 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒) | |
2 | 1 | 3ad2ant2 1168 | 1 ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) ∧ 𝜂) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 386 ∧ w3a 1111 |
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 387 df-3an 1113 |
This theorem is referenced by: btwnconn1lem8 32735 btwnconn1lem9 32736 btwnconn1lem10 32737 btwnconn1lem11 32738 btwnconn1lem12 32739 cdlemj3 36893 jm2.27 38413 iunrelexpmin2 38840 |
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