Theorem exp4d 438

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

Hypothesis

Ref	Expression
exp4d.1	⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏))

Assertion

Ref	Expression
exp4d	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp4d

Step	Hyp	Ref	Expression
1		exp4d.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ (𝜒 ∧ 𝜃)) → 𝜏))
2	1	expd 420	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))
3	2	exp4a 436	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 400

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-an 401

This theorem is referenced by:  tfrlem9  8360  omass  8553  pssnn  9141  cardinfima  10069  ltexprlem7  11015  facdiv  14314  infpnlem1  16960  atcvatlem  32646  mdsymlem5  32668  mdsymlem7  32670  btwnconn1lem11  36460  exp5k  36677