Theorem exp4d 439

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 421	. 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:  tfrlem9  8378  omass  8571  pssnn  9167  cardinfima  10104  ltexprlem7  11055  facdiv  14355  infpnlem1  17008  atcvatlem  32874  mdsymlem5  32896  mdsymlem7  32898  btwnconn1lem11  36685  exp5k  36932