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Mirrors > Home > NFE 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 5127 | . 2 ⊢ (A = B → (Fun A ↔ Fun B)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (Fun A ↔ Fun B) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 = wceq 1642 Fun wfun 4775 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-opab 4623 df-br 4640 df-co 4726 df-cnv 4785 df-fun 4789 |
This theorem is referenced by: funco 5142 funprg 5149 funprgOLD 5150 funcnvuni 5161 funcnvres2 5167 f1co 5264 fun11iun 5305 f10 5316 funoprabg 5583 ovidig 5593 funmpt 5687 enpw1 6062 sbthlem3 6205 |
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