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Theorem simp312 1229
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp312 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)

Proof of Theorem simp312
StepHypRef Expression
1 simp12 1112 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant3 1104 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1054 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 197  df-an 385  df-3an 1056 This theorem is referenced by:  dalemrot  35261  dalem-cly  35275  dath2  35341  cdleme26e  35964  cdleme38m  36068  cdleme38n  36069  cdleme39n  36071  cdlemg28b  36308  cdlemk7  36453  cdlemk11  36454  cdlemk12  36455  cdlemk7u  36475  cdlemk11u  36476  cdlemk12u  36477  cdlemk22  36498  cdlemk23-3  36507  cdlemk25-3  36509
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