Theorem exp44 302

Description: An exportation inference.

Hypothesis

Ref	Expression
exp44.1	⊢ ((φ ∧ ((ψ ∧ χ) ∧ θ)) → τ)

Assertion

Ref	Expression
exp44	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp44

Step	Hyp	Ref	Expression
1		exp44.1	. . 3 ⊢ ((φ ∧ ((ψ ∧ χ) ∧ θ)) → τ)
2	1	exp32 294	. 2 ⊢ (φ → ((ψ ∧ χ) → (θ → τ)))
3	2	exp3a 292	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  po2nr 2135  wefrc 2195  tz7.7 2224  oalimcl 3162  mapunen 3397  reclem3pr 3952  div23t 4240  spansncv 5542  atom1d 5750

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