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Metamath Proof Explorer

Theorem jctild

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

Ref Expression
Hypotheses jctild.1 ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
jctild.2 ⊢ ( 𝜑 → 𝜃 )
Assertion jctild ( 𝜑 → ( 𝜓 → ( 𝜃 ∧ 𝜒 ) ) )

Proof

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