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Mirrors > Home > NFE Home > Th. List > df-fun | GIF version |
Description: Define a function. Definition 10.1 of [Quine] p. 65. For alternate definitions, see dffun2 5119, dffun3 5120, dffun4 5121, dffun5 5122, dffun6 5124, dffun7 5133, dffun8 5134, and dffun9 5135. (Contributed by SF, 5-Jan-2015.) (Revised by Scott Fenton, 14-Apr-2021.) |
Ref | Expression |
---|---|
df-fun | ⊢ (Fun A ↔ (A ∘ ◡A) ⊆ I ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class A | |
2 | 1 | wfun 4775 | . 2 wff Fun A |
3 | 1 | ccnv 4771 | . . . 4 class ◡A |
4 | 1, 3 | ccom 4721 | . . 3 class (A ∘ ◡A) |
5 | cid 4763 | . . 3 class I | |
6 | 4, 5 | wss 3257 | . 2 wff (A ∘ ◡A) ⊆ I |
7 | 2, 6 | wb 176 | 1 wff (Fun A ↔ (A ∘ ◡A) ⊆ I ) |
Colors of variables: wff setvar class |
This definition is referenced by: dffun2 5119 funss 5126 nffun 5130 funi 5137 fun0 5154 f1ococnv2 5309 |
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