Theorem adantlrl

Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)

Hypothesis
adantl2.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge (\tau \wedge \psi) \wedge \chi \rightarrow \theta \)
Proof
l0
simpr
\( \vdash \tau \wedge \psi \rightarrow \psi \)
adantl2.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
sylanl2 l0 _