Theorem 3imp21 1277

Description: The importation inference 3imp 1256 with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.)

Hypothesis

Ref	Expression
3imp21.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Assertion

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

Proof of Theorem 3imp21

Step	Hyp	Ref	Expression
1		3imp21.1	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2	1	3imp 1256	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
3	2	3com12 1269	1 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  sotri3  5526  elfz1b  12409  gausslemma2dlem1a  25090  upgrewlkle2  26502  pthdivtx  26625  clwwlkinwwlk  26905  clwlksfclwwlk  26962  upgr3v3e3cycl  27040  upgr4cycl4dv4e  27045  frgrregord013  27253  ax6e2ndeqALT  39167  fmtnofac2  41481