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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 5146 | . 2 ⊢ (𝐴 = 𝐵 → (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 103 = wceq 1289 ⟶wf 5011 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1381 ax-gen 1383 ax-4 1445 ax-17 1464 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-cleq 2081 df-fn 5018 df-f 5019 |
This theorem is referenced by: fmpt2x 5970 fmpt2 5971 tposf 6037 issmo 6053 tfrcllemsucfn 6118 1fv 9550 fxnn0nninf 9844 iseqfcl 9878 |
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