Theorem 19.27v 1894

Description: Theorem 19.27 of [Margaris] p. 90. (Contributed by NM, 3-Jun-2004.)

Assertion

Ref	Expression
19.27v	⊢ (∀x(φ ∧ ψ) ↔ (∀xφ ∧ ψ))

Distinct variable group:   ψ,x

Allowed substitution hint:   φ(x)

Proof of Theorem 19.27v

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxψ
2	1	19.27 1869	1 ⊢ (∀x(φ ∧ ψ) ↔ (∀xφ ∧ ψ))

Syntax hints:   ↔ wb 176   ∧ wa 358  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545

This theorem is referenced by:  dfuni12  4292