Metamath Proof Explorer


Theorem 3adantr2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005)

Ref Expression
Hypothesis 3adantr.1 φψχθ
Assertion 3adantr2 φψτχθ

Proof

Step Hyp Ref Expression
1 3adantr.1 φψχθ
2 3simpb ψτχψχ
3 2 1 sylan2 φψτχθ