Theorem 19.28v 1895

Description: Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 25-Mar-2004.)

Assertion

Ref	Expression
19.28v	⊢ (∀x(φ ∧ ψ) ↔ (φ ∧ ∀xψ))

Distinct variable group:   φ,x

Allowed substitution hint:   ψ(x)

Proof of Theorem 19.28v

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxφ
2	1	19.28 1870	1 ⊢ (∀x(φ ∧ ψ) ↔ (φ ∧ ∀xψ))

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:  cbval2  2004  reu6  3026