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Mirrors > Home > MPE Home > Th. List > ra4v | Structured version Visualization version GIF version |
Description: Version of ra4 3866 with a disjoint variable condition, requiring fewer axioms. This is stdpc5v 1930 for a restricted domain. (Contributed by BJ, 27-Mar-2020.) |
Ref | Expression |
---|---|
ra4v | ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) → (𝜑 → ∀𝑥 ∈ 𝐴 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.21v 3172 | . 2 ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) ↔ (𝜑 → ∀𝑥 ∈ 𝐴 𝜓)) | |
2 | 1 | biimpi 217 | 1 ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) → (𝜑 → ∀𝑥 ∈ 𝐴 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wral 3135 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 |
This theorem depends on definitions: df-bi 208 df-ex 1772 df-ral 3140 |
This theorem is referenced by: wfr3g 7942 frr3g 33018 |
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