Theorem 3comr 1214

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 1213	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃)
3	2	3coml 1213	1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 981

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 983

This theorem is referenced by:  nnacan  6611  le2tri3i  8201  ltaddsublt  8664  div12ap  8787  lemul12b  8954  zdivadd  9482  zdivmul  9483  elfz  10156  fzmmmeqm  10200  fzrev  10226  absdiflt  11478  absdifle  11479  dvds0lem  12187  dvdsmulc  12205  dvds2add  12211  dvds2sub  12212  dvdstr  12214  lcmdvds  12476  psmettri2  14875  xmettri2  14908