Theorem 3imp21 1193

Description: The importation inference 3imp 1188 with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.) (Revised to shorten 3com12 1202 by Wolf Lammen, 23-Jun-2022.)

Hypothesis

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

Assertion

Ref	Expression
3imp21	⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)

Proof of Theorem 3imp21

Step	Hyp	Ref	Expression
1		3imp31.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	com13 80	. 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃)))
3	2	3imp231 1192	1 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 973

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 975

This theorem is referenced by: (None)