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  6758  le2tri3i  8398  ltaddsublt  8862  div12ap  8985  lemul12b  9152  zdivadd  9685  zdivmul  9686  elfz  10367  fzmmmeqm  10413  fzrev  10440  absdiflt  11802  absdifle  11803  dvds0lem  12512  dvdsmulc  12530  dvds2add  12536  dvds2sub  12537  dvdstr  12539  lcmdvds  12801  psmettri2  15319  xmettri2  15352