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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 5148 | . 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 104 = wceq 1299 Fn wfn 5054 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1391 ax-gen 1393 ax-4 1455 ax-17 1474 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-cleq 2093 df-fn 5062 |
This theorem is referenced by: fnunsn 5166 tpos0 6101 dfixp 6524 ser0f 10129 |
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