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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 ) ) )