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Theorem 19.28v 1873
Description: Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
19.28v (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem 19.28v
StepHypRef Expression
1 ax-17 1507 . 2 (𝜑 → ∀𝑥𝜑)
2119.28h 1542 1 (∀𝑥(𝜑𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104  wal 1330
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-4 1488  ax-17 1507
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  reu6  2876  dfer2  6437
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