Theorem imp4a 341

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

Hypothesis

Ref	Expression
imp4.1	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Assertion

Ref	Expression
imp4a	⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))

Proof of Theorem imp4a

Step	Hyp	Ref	Expression
1		imp4.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2		impexp 259	. 2 ⊢ (((𝜒 ∧ 𝜃) → 𝜏) ↔ (𝜒 → (𝜃 → 𝜏)))
3	1, 2	syl6ibr 160	1 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))

Syntax hints:   → wi 4   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  imp4b  342  imp4d  344  imp55  353  imp511  354  equs5or  1758  reuss2  3279  tfrlem9  6084  facwordi  10144  ndvdssub  11204