Theorem exp45 303

Description: An exportation inference.

Hypothesis

Ref	Expression
exp45.1	⊢ ((φ ∧ (ψ ∧ (χ ∧ θ))) → τ)

Assertion

Ref	Expression
exp45	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp45

Step	Hyp	Ref	Expression
1		exp45.1	. . 3 ⊢ ((φ ∧ (ψ ∧ (χ ∧ θ))) → τ)
2	1	exp32 294	. 2 ⊢ (φ → (ψ → ((χ ∧ θ) → τ)))
3	2	exp4a 295	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  oaass 3163  zornlem4 3606  zornlem7 3609  spansncv 5542  mdsymlem5 5780

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