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Mirrors > Home > ILE Home > Th. List > endomtr | Unicode version |
Description: Transitivity of equinumerosity and dominance. (Contributed by NM, 7-Jun-1998.) |
Ref | Expression |
---|---|
endomtr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | endom 6741 | . 2 | |
2 | domtr 6763 | . 2 | |
3 | 1, 2 | sylan 281 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 class class class wbr 3989 cen 6716 cdom 6717 |
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 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-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 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-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-fun 5200 df-fn 5201 df-f 5202 df-f1 5203 df-f1o 5205 df-en 6719 df-dom 6720 |
This theorem is referenced by: cnvct 6787 xpdom1g 6811 xpdom3m 6812 domen1 6820 mapdom1g 6825 phplem4dom 6840 phpm 6843 fict 6846 fisbth 6861 fientri3 6892 difinfsn 7077 pw1dom2 7204 qnnen 12386 nninfdc 12408 |
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