Theorem imdistanda

Description: Distribution of implication with conjunction (deduction version with conjoined antecedent). (Contributed by Jeff Madsen, 19-Jun-2011)

	Ref	Expression
Hypothesis	imdistanda.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
Assertion	imdistanda	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imdistanda.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
2	1	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	imdistand	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜃 ) ) )