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Mirrors > Home > MPE Home > Th. List > fnfund | Structured version Visualization version GIF version |
Description: A function with domain is a function, deduction form. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
fnfund.1 | ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Ref | Expression |
---|---|
fnfund | ⊢ (𝜑 → Fun 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnfund.1 | . 2 ⊢ (𝜑 → 𝐹 Fn 𝐴) | |
2 | fnfun 6603 | . 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 6491 Fn wfn 6492 |
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 206 df-an 398 df-fn 6500 |
This theorem is referenced by: bnj945 33388 bnj545 33510 bnj548 33512 bnj553 33513 bnj570 33520 bnj929 33551 bnj966 33559 bnj1442 33664 bnj1450 33665 bnj1501 33682 imadrhmcl 40719 |
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