Theorem 3comr 1238

Description: Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996.)

Hypothesis

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

Assertion

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

Proof of Theorem 3comr

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3coml 1237	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃)
3	2	3coml 1237	1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1007

This theorem is referenced by:  nnacan  6745  le2tri3i  8382  ltaddsublt  8845  div12ap  8968  lemul12b  9135  zdivadd  9667  zdivmul  9668  elfz  10348  fzmmmeqm  10392  fzrev  10418  absdiflt  11777  absdifle  11778  dvds0lem  12487  dvdsmulc  12505  dvds2add  12511  dvds2sub  12512  dvdstr  12514  lcmdvds  12776  psmettri2  15193  xmettri2  15226