Theorem exp45 444

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

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 426	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))
3	2	exp4a 437	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  oaass  8555  zorn2lem4  10501  zorn2lem7  10504  iscatd2  17762  fgss2  24068  alexsubALTlem4  24244  grporcan  30907  spansncvi  32041  mdsymlem5  32796  riotasv3d  39775  cvratlem  40236  hbtlem2  43892