Metamath Proof Explorer


Theorem 3ad2antr1

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 25-Dec-2007)

Ref Expression
Hypothesis 3ad2antl.1 φ χ θ
Assertion 3ad2antr1 φ χ ψ τ θ

Proof

Step Hyp Ref Expression
1 3ad2antl.1 φ χ θ
2 1 adantrr φ χ ψ θ
3 2 3adantr3 φ χ ψ τ θ