Theorem ex3 1365

Description: Apply ex 418 to a hypothesis with a 3-right-nested conjunction antecedent, with the antecedent of the assertion being a triple conjunction rather than a 2-right-nested conjunction. (Contributed by Alan Sare, 22-Apr-2018.)

Hypothesis

Ref	Expression
ex3.1	⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
ex3	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → 𝜏))

Proof of Theorem ex3

Step	Hyp	Ref	Expression
1		ex3.1	. . 3 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
2	1	ex 418	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → (𝜃 → 𝜏))
3	2	3impa 1127	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → (𝜃 → 𝜏))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  fzrevral  13659  pthdepisspth  30121  cyc3genpm  33503  iunconnlem2  45684