Theorem an1s 372

Description: Deduction rearranging conjuncts.

Hypothesis

Ref	Expression
an1s.1	⊢ ((φ ∧ (ψ ∧ χ)) → θ)

Assertion

Ref	Expression
an1s	⊢ ((ψ ∧ (φ ∧ χ)) → θ)

Proof of Theorem an1s

Step	Hyp	Ref	Expression
1		an12 370	. 2 ⊢ ((ψ ∧ (φ ∧ χ)) ↔ (φ ∧ (ψ ∧ χ)))
2		an1s.1	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	1, 2	sylbi 174	1 ⊢ ((ψ ∧ (φ ∧ χ)) → θ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  oecl 3140  oaass 3163  oen0 3165  ac5b 3574  distrlem4pr 3924  prlem934b 3932  ltexprlem4 3939  uzind2 4604  spansnmul 5469

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org