Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > funeqi | GIF version |
Description: Equality inference for the function predicate. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
funeqi.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
funeqi | ⊢ (Fun 𝐴 ↔ Fun 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funeqi.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | funeq 5113 | . 2 ⊢ (𝐴 = 𝐵 → (Fun 𝐴 ↔ Fun 𝐵)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (Fun 𝐴 ↔ Fun 𝐵) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 = wceq 1316 Fun wfun 5087 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-in 3047 df-ss 3054 df-br 3900 df-opab 3960 df-rel 4516 df-cnv 4517 df-co 4518 df-fun 5095 |
This theorem is referenced by: funmpt 5131 funmpt2 5132 funprg 5143 funtpg 5144 funtp 5146 funcnvuni 5162 f1cnvcnv 5309 f1co 5310 fun11iun 5356 f10 5369 funoprabg 5838 mpofun 5841 ovidig 5856 tposfun 6125 tfri1dALT 6216 tfrcl 6229 rdgfun 6238 frecfun 6260 frecfcllem 6269 th3qcor 6501 ssdomg 6640 sbthlem7 6819 sbthlemi8 6820 casefun 6938 caseinj 6942 djufun 6957 djuinj 6959 ctssdccl 6964 axaddf 7644 axmulf 7645 strleund 11974 strleun 11975 1strbas 11985 2strbasg 11987 2stropg 11988 |
Copyright terms: Public domain | W3C validator |