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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj930 | 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 |
---|---|
bnj930.1 | ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Ref | Expression |
---|---|
bnj930 | ⊢ (𝜑 → Fun 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj930.1 | . 2 ⊢ (𝜑 → 𝐹 Fn 𝐴) | |
2 | fnfun 6423 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → Fun 𝐹) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Fun wfun 6318 Fn wfn 6319 |
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-an 400 df-fn 6327 |
This theorem is referenced by: bnj945 32155 bnj545 32277 bnj548 32279 bnj553 32280 bnj570 32287 bnj929 32318 bnj966 32326 bnj1442 32431 bnj1450 32432 bnj1501 32449 |
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