Theorem exp4d 637

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 452	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))
3	2	exp4a 633	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 384

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 197  df-an 386

This theorem is referenced by:  tfrlem9  7481  omass  7660  pssnn  8178  cardinfima  8920  ltexprlem7  9864  facdiv  13074  infpnlem1  15614  atcvatlem  29244  mdsymlem5  29266  mdsymlem7  29268  btwnconn1lem11  32204  exp5k  32298