Theorem exp516 1229

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)

Hypothesis

Ref	Expression
exp516.1	⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
exp516	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Proof of Theorem exp516

Step	Hyp	Ref	Expression
1		exp516.1	. . 3 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂)
2	1	exp31 364	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜏 → 𝜂)))
3	2	3expd 1226	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂)))))

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by: (None)