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Metamath Proof Explorer

Theorem jca3

Description: Inference conjoining the consequents of two implications. (Contributed by Rodolfo Medina, 14-Oct-2010)

Ref Expression
Hypotheses jca3.1 ⊢ φ → ψ → χ
jca3.2 ⊢ θ → τ
Assertion jca3 ⊢ φ → ψ → θ → χ ∧ τ

Proof

Step Hyp Ref Expression
1 jca3.1 ⊢ φ → ψ → χ
2 jca3.2 ⊢ θ → τ
3 1 imp ⊢ φ ∧ ψ → χ
4 3 a1d ⊢ φ ∧ ψ → θ → χ
5 4 2 jca2 ⊢ φ ∧ ψ → θ → χ ∧ τ
6 5 ex ⊢ φ → ψ → θ → χ ∧ τ