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Mirrors > Home > MPE Home > Th. List > ra4v | Structured version Visualization version GIF version |
Description: Version of ra4 3798 with a disjoint variable condition, requiring fewer axioms. This is stdpc5v 1946 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 3098 | . 2 ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) ↔ (𝜑 → ∀𝑥 ∈ 𝐴 𝜓)) | |
2 | 1 | biimpi 219 | 1 ⊢ (∀𝑥 ∈ 𝐴 (𝜑 → 𝜓) → (𝜑 → ∀𝑥 ∈ 𝐴 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wral 3061 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 |
This theorem depends on definitions: df-bi 210 df-ex 1788 df-ral 3066 |
This theorem is referenced by: wfr3g 8053 frr3g 9372 |
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