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Mirrors > Home > ILE Home > Th. List > op2ndd | Unicode version |
Description: Extract the second member of an ordered pair. (Contributed by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
op1st.1 | |
op1st.2 |
Ref | Expression |
---|---|
op2ndd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 5414 | . 2 | |
2 | op1st.1 | . . 3 | |
3 | op1st.2 | . . 3 | |
4 | 2, 3 | op2nd 6038 | . 2 |
5 | 1, 4 | syl6eq 2186 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 cvv 2681 cop 3525 cfv 5118 c2nd 6030 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-rn 4545 df-iota 5083 df-fun 5120 df-fv 5126 df-2nd 6032 |
This theorem is referenced by: xp2nd 6057 sbcopeq1a 6078 csbopeq1a 6079 eloprabi 6087 mpomptsx 6088 dmmpossx 6090 fmpox 6091 fmpoco 6106 df2nd2 6110 xporderlem 6121 xpf1o 6731 frecuzrdgtcl 10178 frecuzrdgfunlem 10185 fisumcom2 11200 txbas 12416 cnmpt2nd 12447 txhmeo 12477 |
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