Theorem 19.28v 1301

Description: Theorem 19.28 of [Margaris] p. 90.

Assertion

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

Distinct variable group:   φ,x

Proof of Theorem 19.28v

Step	Hyp	Ref	Expression
1		ax-17 973	. 2 ⊢ (φ → ∀xφ)
2	1	19.28 1072	1 ⊢ (∀x(φ ⋀ ψ) ↔ (φ ⋀ ∀xψ))

Syntax hints:   ↔ wb 146   ⋀ wa 223  ∀wal 956

This theorem is referenced by:  reu3 1934  iinss 2604  tfrlem2 3918  dfer2 4268  kmlem14 4788  kmlem15 4789

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-an 225

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