Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > feq23i | GIF version |
Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011.) |
Ref | Expression |
---|---|
feq23i.1 | ⊢ 𝐴 = 𝐶 |
feq23i.2 | ⊢ 𝐵 = 𝐷 |
Ref | Expression |
---|---|
feq23i | ⊢ (𝐹:𝐴⟶𝐵 ↔ 𝐹:𝐶⟶𝐷) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq23i.1 | . 2 ⊢ 𝐴 = 𝐶 | |
2 | feq23i.2 | . 2 ⊢ 𝐵 = 𝐷 | |
3 | feq23 5253 | . 2 ⊢ ((𝐴 = 𝐶 ∧ 𝐵 = 𝐷) → (𝐹:𝐴⟶𝐵 ↔ 𝐹:𝐶⟶𝐷)) | |
4 | 1, 2, 3 | mp2an 422 | 1 ⊢ (𝐹:𝐴⟶𝐵 ↔ 𝐹:𝐶⟶𝐷) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 = wceq 1331 ⟶wf 5114 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-in 3072 df-ss 3079 df-fn 5121 df-f 5122 |
This theorem is referenced by: ftpg 5597 |
Copyright terms: Public domain | W3C validator |