Theorem adantrr

Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)

Hypothesis
adant2.1
\( \vdash \varphi \wedge \psi \rightarrow \chi \)
Conclusion
\( \vdash \varphi \wedge (\psi \wedge \theta) \rightarrow \chi \)
Proof
l0
simpl
\( \vdash \psi \wedge \theta \rightarrow \psi \)
adant2.1
\( \vdash \varphi \wedge \psi \rightarrow \chi \)
sylan2 l0 _