Theorem simplbda 607

Description: Deduction eliminating a conjunct. (Contributed by NM, 22-Oct-2007.)

Hypothesis

Ref	Expression
pm3.26bda.1	⊢ (φ → (ψ ↔ (χ ∧ θ)))

Assertion

Ref	Expression
simplbda	⊢ ((φ ∧ ψ) → θ)

Proof of Theorem simplbda

Step	Hyp	Ref	Expression
1		pm3.26bda.1	. . 3 ⊢ (φ → (ψ ↔ (χ ∧ θ)))
2	1	biimpa 470	. 2 ⊢ ((φ ∧ ψ) → (χ ∧ θ))
3	2	simprd 449	1 ⊢ ((φ ∧ ψ) → θ)

Syntax hints:   → wi 4   ↔ wb 176   ∧ 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)