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Metamath Proof Explorer

Theorem jctird

Description: Deduction conjoining a theorem to right of consequent in an implication. (Contributed by NM, 21-Apr-2005)

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

Proof

Step Hyp Ref Expression
1 jctird.1 ⊢ φ → ψ → χ
2 jctird.2 ⊢ φ → θ
3 2 a1d ⊢ φ → ψ → θ
4 1 3 jcad ⊢ φ → ψ → χ ∧ θ