Theorem biimp3ar 1282

Description: Infer implication from a logical equivalence. Similar to biimpar 471. (Contributed by NM, 2-Jan-2009.)

Hypothesis

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

Assertion

Ref	Expression
biimp3ar	⊢ ((φ ∧ ψ ∧ θ) → χ)

Proof of Theorem biimp3ar

Step	Hyp	Ref	Expression
1		biimp3a.1	. . 3 ⊢ ((φ ∧ ψ) → (χ ↔ θ))
2	1	exbiri 605	. 2 ⊢ (φ → (ψ → (θ → χ)))
3	2	3imp 1145	1 ⊢ ((φ ∧ ψ ∧ θ) → χ)

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is used by:  rmoi  3136  ovmpt2x  5713  ceclr  6188