Theorem 3com23 1157

Description: Commutation in antecedent. Swap 2nd and 3rd. (Contributed by NM, 28-Jan-1996.)

Hypothesis

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

Assertion

Ref	Expression
3com23	⊢ ((φ ∧ χ ∧ ψ) → θ)

Proof of Theorem 3com23

Step	Hyp	Ref	Expression
1		3exp.1	. . . 4 ⊢ ((φ ∧ ψ ∧ χ) → θ)
2	1	3exp 1150	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	com23 72	. 2 ⊢ (φ → (χ → (ψ → θ)))
4	3	3imp 1145	1 ⊢ ((φ ∧ χ ∧ ψ) → 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  syld3an2  1229  3anidm13  1240  eqreu  3029