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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj946 | Structured version Visualization version GIF version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj946.1 | ⊢ (𝜑 ↔ ∀𝑥 ∈ 𝐴 𝜓) |
Ref | Expression |
---|---|
bnj946 | ⊢ (𝜑 ↔ ∀𝑥(𝑥 ∈ 𝐴 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj946.1 | . 2 ⊢ (𝜑 ↔ ∀𝑥 ∈ 𝐴 𝜓) | |
2 | df-ral 3058 | . 2 ⊢ (∀𝑥 ∈ 𝐴 𝜓 ↔ ∀𝑥(𝑥 ∈ 𝐴 → 𝜓)) | |
3 | 1, 2 | bitri 278 | 1 ⊢ (𝜑 ↔ ∀𝑥(𝑥 ∈ 𝐴 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ∀wal 1540 ∈ wcel 2113 ∀wral 3053 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 210 df-ral 3058 |
This theorem is referenced by: bnj1379 32381 bnj570 32456 bnj571 32457 |
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