Theorem 3com13 1198

Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.)

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		3anrev 978	. 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒))
2		3exp.1	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
3	1, 2	sylbi 120	1 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by:  3coml  1200  3adant3l  1224  3adant3r  1225  syld3an1  1274  oaword1  6439  nnacan  6480  elmapg  6627  subadd  8101  xrltso  9732  iooshf  9888  dvdsmulc  11759  lcmdvdsb  12016  infpnlem1  12289