Theorem 19.28v 957

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

Assertion

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

Distinct variable group(s):   φ,x

Proof of Theorem 19.28v

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 ⊢ (φ → ∀xφ)
2	1	19.28 751	1 ⊢ (∀x(φ ∧ ψ) ↔ (φ ∧ ∀xψ))

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

This theorem is referenced by:  iinss 2025  tfrlem2 2950  er2 3201  kmlem14 3593  kmlem15 3594

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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