Theorem 3impexpbicomi 1368

Description: Deduction form of 3impexpbicom 1367. Derived automatically from 3impexpbicomiVD in set.mm. (Contributed by Alan Sare, 31-Dec-2011.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Hypothesis

Ref	Expression
3impexpbicomi.1	⊢ ((φ ∧ ψ ∧ χ) → (θ ↔ τ))

Assertion

Ref	Expression
3impexpbicomi	⊢ (φ → (ψ → (χ → (τ ↔ θ))))

Proof of Theorem 3impexpbicomi

Step	Hyp	Ref	Expression
1		3impexpbicomi.1	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → (θ ↔ τ))
2	1	bicomd 192	. 2 ⊢ ((φ ∧ ψ ∧ χ) → (τ ↔ θ))
3	2	3exp 1150	1 ⊢ (φ → (ψ → (χ → (τ ↔ θ))))

This proof depends on syntax axioms:   → wi 4   ↔ wb 176   ∧ 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: (None)