Theorem 3adant3r

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
\( \vdash \varphi \wedge \psi \wedge \chi \wedge \tau \rightarrow \theta \)
Proof
l0
simpl
\( \vdash \chi \wedge \tau \rightarrow \chi \)
ad4ant3.1
\( \vdash \varphi \wedge \psi \wedge \chi \rightarrow \theta \)
syl3an3 l0 _