Theorem 3adant2l

Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 25-Jun-2022.)

Hypothesis
ad4ant3.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
Conclusion
\( \vdash \varphi \wedge \tau \wedge \psi \wedge \chi \rightarrow \theta \)
Proof
l0
simpr
\( \vdash \tau \wedge \psi \rightarrow \psi \)
ad4ant3.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
syl3an2 l0 _