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Mirrors > Home > ILE Home > Th. List > fneq2i | GIF version |
Description: Equality inference for function predicate with domain. (Contributed by NM, 4-Sep-2011.) |
Ref | Expression |
---|---|
fneq2i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
fneq2i | ⊢ (𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq2i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | fneq2 4988 | . 2 ⊢ (𝐴 = 𝐵 → (𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐹 Fn 𝐴 ↔ 𝐹 Fn 𝐵) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 = wceq 1243 Fn wfn 4897 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-4 1400 ax-17 1419 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-fn 4905 |
This theorem is referenced by: fnunsn 5006 tpos0 5889 iser0f 9251 |
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