Theorem 3imp31 1178

Description: The importation inference 3imp 1176 with commutation of the first and third conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.)

Hypothesis

Ref	Expression
3imp31.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Assertion

Ref	Expression
3imp31	⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Proof of Theorem 3imp31

Step	Hyp	Ref	Expression
1		3imp31.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	com13 80	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
3	2	3imp 1176	1 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 963

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

This theorem depends on definitions:  df-bi 116  df-3an 965

This theorem is referenced by:  dvdsmodexp  11684