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Metamath Proof Explorer

Theorem jca2r

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 17-Oct-2010)

Ref Expression
Hypotheses jca2r.1 ⊢ φ → ψ → χ
jca2r.2 ⊢ ψ → θ
Assertion jca2r ⊢ φ → ψ → θ ∧ χ

Proof

Step Hyp Ref Expression
1 jca2r.1 ⊢ φ → ψ → χ
2 jca2r.2 ⊢ ψ → θ
3 2 a1i ⊢ φ → ψ → θ
4 3 1 jcad ⊢ φ → ψ → θ ∧ χ