Theorem biimp3a 1281

Description: Infer implication from a logical equivalence. Similar to biimpa 470. (Contributed by NM, 4-Sep-2005.)

Hypothesis

Ref	Expression
biimp3a.1	⊢ ((φ ∧ ψ) → (χ ↔ θ))

Assertion

Ref	Expression
biimp3a	⊢ ((φ ∧ ψ ∧ χ) → θ)

Proof of Theorem biimp3a

Step	Hyp	Ref	Expression
1		biimp3a.1	. . 3 ⊢ ((φ ∧ ψ) → (χ ↔ θ))
2	1	biimpa 470	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
3	2	3impa 1146	1 ⊢ ((φ ∧ ψ ∧ χ) → θ)

Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is referenced by: (None)