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Theorem simp312 1320
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 1203 . 2 (((𝜑𝜓𝜒) ∧ 𝜃𝜏) → 𝜓)
213ad2ant3 1134 1 ((𝜂𝜁 ∧ ((𝜑𝜓𝜒) ∧ 𝜃𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  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 207  df-an 396  df-3an 1088
This theorem is referenced by:  dalemrot  39640  dalem-cly  39654  dath2  39720  cdleme26e  40342  cdleme38m  40446  cdleme38n  40447  cdleme39n  40449  cdlemg28b  40686  cdlemk7  40831  cdlemk11  40832  cdlemk12  40833  cdlemk7u  40853  cdlemk11u  40854  cdlemk12u  40855  cdlemk22  40876  cdlemk23-3  40885  cdlemk25-3  40887
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