Theorem impl 603

Description: Export a wff from a left conjunct. (Contributed by Mario Carneiro, 9-Jul-2014.)

Hypothesis

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

Assertion

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

Proof of Theorem impl

Step	Hyp	Ref	Expression
1		impl.1	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
2	1	exp3a 425	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imp31 421	1 ⊢ (((φ ∧ ψ) ∧ χ) → θ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  sbc2iedv  3115  csbie2t  3181  foco2  5427