Theorem 19.27v 956

Description: Theorem 19.27 of [Margaris] p. 90.

Assertion

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

Distinct variable group(s):   ψ,x

Proof of Theorem 19.27v

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (ψ → ∀xψ)
2	1	19.27 750	1 ⊢ (∀x(φ ∧ ψ) ↔ (∀xφ ∧ ψ))

Syntax hints:   ↔ wb 127   ∧ wa 196  ∀wal 672

This theorem is referenced by:  r19.27av 1293

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

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

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