Theorem 19.27v 1820

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		ax-17 1459	. 2 ⊢ (𝜓 → ∀𝑥𝜓)
2	1	19.27h 1492	1 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (∀𝑥𝜑 ∧ 𝜓))

Syntax hints:   ∧ wa 102   ↔ wb 103  ∀wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-4 1440  ax-17 1459

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)