Theorem ancom2s 777

Description: Inference commuting a nested conjunction in antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)

Hypothesis

Ref	Expression
an12s.1	⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Assertion

Ref	Expression
ancom2s	⊢ ((φ ∧ (χ ∧ ψ)) → θ)

Proof of Theorem ancom2s

Step	Hyp	Ref	Expression
1		pm3.22 436	. 2 ⊢ ((χ ∧ ψ) → (ψ ∧ χ))
2		an12s.1	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	1, 2	sylan2 460	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:  an42s  800  xpexr2  5111  f1elima  5475