Theorem 3com13 1156

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 945	. 2 ⊢ ((χ ∧ ψ ∧ φ) ↔ (φ ∧ ψ ∧ χ))
2		3exp.1	. 2 ⊢ ((φ ∧ ψ ∧ χ) → θ)
3	1, 2	sylbi 187	1 ⊢ ((χ ∧ ψ ∧ 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:  3coml  1158  3adant3l  1178  3adant3r  1179  syld3an1  1228