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Mirrors > Home > ILE Home > Th. List > prodeq1i | Unicode version |
Description: Equality inference for product. (Contributed by Scott Fenton, 4-Dec-2017.) |
Ref | Expression |
---|---|
prodeq1i.1 |
Ref | Expression |
---|---|
prodeq1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | prodeq1i.1 | . 2 | |
2 | prodeq1 11503 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 cprod 11500 |
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-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-dc 830 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-if 3526 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-mpt 4050 df-cnv 4617 df-dm 4619 df-rn 4620 df-res 4621 df-iota 5158 df-f 5200 df-f1 5201 df-fo 5202 df-f1o 5203 df-fv 5204 df-ov 5853 df-oprab 5854 df-mpo 5855 df-recs 6281 df-frec 6367 df-seqfrec 10389 df-proddc 11501 |
This theorem is referenced by: prodeq12i 11513 fprodfac 11565 fprodxp 11574 |
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