Theorem exp41 299

Description: An exportation inference.

Hypothesis

Ref	Expression
exp41.1	⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → τ)

Assertion

Ref	Expression
exp41	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp41

Step	Hyp	Ref	Expression
1		exp41.1	. . 3 ⊢ ((((φ ∧ ψ) ∧ χ) ∧ θ) → τ)
2	1	exp 291	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → (θ → τ))
3	2	exp31 293	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  tz7.49 2997  infxpidmlem12 4944  osumlem4 5533

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org