Theorem 3coml 1158

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

Hypothesis

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

Assertion

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

Proof of Theorem 3coml

Step	Hyp	Ref	Expression
1		3exp.1	. . 3 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3com23 1157	. 2 ⊢ ((φ ∧ χ ∧ ψ) → θ)
3	2	3com13 1156	1 ⊢ ((ψ ∧ χ ∧ φ) → θ)

Syntax hints:   → wi 4   ∧ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by:  3comr  1159  addccan1  4561  addcdir  6252