Theorem anass1rs 782

Description: Commutative-associative law for conjunction in an antecedent. (Contributed by Jeff Madsen, 19-Jun-2011.)

Hypothesis

Ref	Expression
anass1rs.1	⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Assertion

Ref	Expression
anass1rs	⊢ (((φ ∧ χ) ∧ ψ) → θ)

Proof of Theorem anass1rs

Step	Hyp	Ref	Expression
1		anass1rs.1	. . 3 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
2	1	anassrs 629	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
3	2	an32s 779	1 ⊢ (((φ ∧ χ) ∧ ψ) → θ)

Syntax hints:   → wi 4   ∧ wa 358

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

This theorem is referenced by: (None)