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Mirrors > Home > ILE Home > Th. List > fveq1i | GIF version |
Description: Equality inference for function value. (Contributed by NM, 2-Sep-2003.) |
Ref | Expression |
---|---|
fveq1i.1 | ⊢ 𝐹 = 𝐺 |
Ref | Expression |
---|---|
fveq1i | ⊢ (𝐹‘𝐴) = (𝐺‘𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1i.1 | . 2 ⊢ 𝐹 = 𝐺 | |
2 | fveq1 5304 | . 2 ⊢ (𝐹 = 𝐺 → (𝐹‘𝐴) = (𝐺‘𝐴)) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐹‘𝐴) = (𝐺‘𝐴) |
Colors of variables: wff set class |
Syntax hints: = wceq 1289 ‘cfv 5015 |
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-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-uni 3654 df-br 3846 df-iota 4980 df-fv 5023 |
This theorem is referenced by: fveq12i 5311 fvun2 5371 fvopab3ig 5378 fvsnun1 5494 fvsnun2 5495 fvpr1 5501 fvpr2 5502 fvpr1g 5503 fvpr2g 5504 fvtp1g 5505 fvtp2g 5506 fvtp3g 5507 fvtp2 5509 fvtp3 5510 ov 5764 ovigg 5765 ovg 5783 tfr2a 6086 tfrex 6133 frec0g 6162 freccllem 6167 frecsuclem 6171 addpiord 6875 mulpiord 6876 fseq1p1m1 9508 frec2uz0d 9806 frec2uzzd 9807 frec2uzsucd 9808 frecuzrdgrrn 9815 frec2uzrdg 9816 frecuzrdg0 9820 frecuzrdgsuc 9821 frecuzrdgg 9823 frecuzrdg0t 9829 frecuzrdgsuctlem 9830 0tonninf 9845 1tonninf 9846 inftonninf 9847 iseqvalt 9873 seq3val 9874 hashinfom 10186 hashennn 10188 hashfz1 10191 shftidt 10267 resqrexlemf1 10441 resqrexlemfp1 10442 cbvsum 10749 fisumss 10784 fsumadd 10800 isumclim3 10817 ialgr0 11304 ialgrp1 11306 ndxarg 11519 strslfv2d 11536 |
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