Theorem a1ddd 78

Description: Triple deduction introducing an antecedent to a wff. Deduction associated with a1dd 48. Double deduction associated with a1d 25. Triple deduction associated with ax-1 6 and a1i 11. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypothesis

Ref	Expression
a1ddd.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))

Assertion

Ref	Expression
a1ddd	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem a1ddd

Step	Hyp	Ref	Expression
1		a1ddd.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
2		ax-1 6	. 2 ⊢ (𝜏 → (𝜃 → 𝜏))
3	1, 2	syl8 74	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  ad4ant123  1286  ad5ant13  1293  ad5ant14  1294  ad5ant15  1295  ad5ant23  1296  ad5ant24  1297  ad5ant25  1298  ad5ant234  1300  ad5ant235  1301  ad5ant123  1302  ad5ant124  1303  ad5ant134  1305  ad5ant135  1306