Theorem 3com12 1155

Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Hypothesis

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

Assertion

Ref	Expression
3com12	⊢ ((ψ ∧ φ ∧ χ) → θ)

Proof of Theorem 3com12

Step	Hyp	Ref	Expression
1		3ancoma 941	. 2 ⊢ ((ψ ∧ φ ∧ χ) ↔ (φ ∧ ψ ∧ χ))
2		3exp.1	. 2 ⊢ ((φ ∧ ψ ∧ χ) → θ)
3	1, 2	sylbi 187	1 ⊢ ((ψ ∧ φ ∧ χ) → 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:  3adant2l  1176  3adant2r  1177  fvun2  5381