Theorem imdistanda 674

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

Hypothesis

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

Assertion

Ref	Expression
imdistanda	⊢ (φ → ((ψ ∧ χ) → (ψ ∧ θ)))

Proof of Theorem imdistanda

Step	Hyp	Ref	Expression
1		imdistanda.1	. . 3 ⊢ ((φ ∧ ψ) → (χ → θ))
2	1	ex 423	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imdistand 673	1 ⊢ (φ → ((ψ ∧ χ) → (ψ ∧ θ)))

Syntax hints:   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by: (None)