Theorem exp4a 364

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

Hypothesis

Ref	Expression
exp4a.1	⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))

Assertion

Ref	Expression
exp4a	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp4a

Step	Hyp	Ref	Expression
1		exp4a.1	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))
2		impexp 261	. 2 ⊢ (((𝜒 ∧ 𝜃) → 𝜏) ↔ (𝜒 → (𝜃 → 𝜏)))
3	1, 2	syl6ib 160	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  exp4b  365  exp4d  367  exp45  372  exp5c  374  tfri3  6335  nnmordi  6484  fiintim  6894  ndvdssub  11867  iscnp4  12868  metcnp3  13161