Theorem imp4aOLD 615

Description: Obsolete proof of imp4a 614 as of 19-Jul-2021. (Contributed by NM, 26-Apr-1994.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
imp4aOLD	⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))

Proof of Theorem imp4aOLD

Step	Hyp	Ref	Expression
1		imp4.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
2		impexp 462	. 2 ⊢ (((𝜒 ∧ 𝜃) → 𝜏) ↔ (𝜒 → (𝜃 → 𝜏)))
3	1, 2	syl6ibr 242	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: (None)