Theorem 3com13 1124

Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Wolf Lammen, 22-Jun-2022.)

Hypothesis

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

Assertion

Ref	Expression
3com13	⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Proof of Theorem 3com13

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3exp 1119	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	3imp31 1111	1 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1086

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  3comr  1125  3coml  1127  oacan  8489  oaword1  8493  nnacan  8569  nnaword1  8570  elmapg  8789  fisseneq  9180  ltapr  10974  subadd  11400  ltaddsub  11628  leaddsub  11630  iooshf  13363  faclbnd4  14238  relexpsucl  14973  relexpsucr  14974  dvdsmulc  16229  lcmdvdsb  16559  infpnlem1  16857  fmf  23808  frgr3v  30177  nvs  30565  dipdi  30745  dipsubdi  30751  spansncol  31470  chirredlem2  32293  mdsymlem3  32307  isbasisrelowllem2  37317  ltflcei  37575  iscringd  37965  resubadd  42340  iunrelexp0  43664  uun123p4  44774  isosctrlem1ALT  44896  stoweidlem17  45988