Metamath Proof Explorer


Theorem adantrr

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

Ref Expression
Hypothesis adant2.1 φψχ
Assertion adantrr φψθχ

Proof

Step Hyp Ref Expression
1 adant2.1 φψχ
2 simpl ψθψ
3 2 1 sylan2 φψθχ