Theorem adantllr

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
simpl
\( \vdash \varphi \wedge \tau \rightarrow \varphi \)
adantl2.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
sylanl1 l0 _