Theorem expl 601

Description: Export a wff from a left conjunct. (Contributed by Jeff Hankins, 28-Aug-2009.)

Hypothesis

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

Assertion

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

Proof of Theorem expl

Step	Hyp	Ref	Expression
1		expl.1	. . 3 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
2	1	exp31 587	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	imp3a 420	1 ⊢ (φ → ((ψ ∧ χ) → 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)