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Axiom ax-4 1734
Description: Axiom of Quantified Implication. Axiom C4 of [Monk2] p. 105 and Theorem 19.20 of [Margaris] p. 90. It is restated as alim 1735 for labeling consistency. It should be used only by alim 1735. (Contributed by NM, 21-May-2008.) Use alim 1735 instead. (New usage is discouraged.)
Assertion
Ref Expression
ax-4 (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))

Detailed syntax breakdown of Axiom ax-4
StepHypRef Expression
1 wph . . . 4 wff 𝜑
2 wps . . . 4 wff 𝜓
31, 2wi 4 . . 3 wff (𝜑𝜓)
4 vx . . 3 setvar 𝑥
53, 4wal 1478 . 2 wff 𝑥(𝜑𝜓)
61, 4wal 1478 . . 3 wff 𝑥𝜑
72, 4wal 1478 . . 3 wff 𝑥𝜓
86, 7wi 4 . 2 wff (∀𝑥𝜑 → ∀𝑥𝜓)
95, 8wi 4 1 wff (∀𝑥(𝜑𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓))
Colors of variables: wff setvar class
This axiom is referenced by:  alim  1735
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