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Mirrors > Home > ILE Home > Th. List > feq2i | GIF version |
Description: Equality inference for functions. (Contributed by NM, 5-Sep-2011.) |
Ref | Expression |
---|---|
feq2i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
feq2i | ⊢ (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq2i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | feq2 5226 | . 2 ⊢ (𝐴 = 𝐵 → (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 = wceq 1316 ⟶wf 5089 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-4 1472 ax-17 1491 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-fn 5096 df-f 5097 |
This theorem is referenced by: fmpox 6066 fmpo 6067 tposf 6137 issmo 6153 tfrcllemsucfn 6218 1fv 9884 fxnn0nninf 10179 0met 12480 dvef 12783 |
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