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Mirrors > Home > ILE Home > Th. List > 2ndvalg | Unicode version |
Description: The value of the function that extracts the second member of an ordered pair. (Contributed by NM, 9-Oct-2004.) (Revised by Mario Carneiro, 8-Sep-2013.) |
Ref | Expression |
---|---|
2ndvalg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snexg 4170 | . . 3 | |
2 | rnexg 4876 | . . 3 | |
3 | uniexg 4424 | . . 3 | |
4 | 1, 2, 3 | 3syl 17 | . 2 |
5 | sneq 3594 | . . . . 5 | |
6 | 5 | rneqd 4840 | . . . 4 |
7 | 6 | unieqd 3807 | . . 3 |
8 | df-2nd 6120 | . . 3 | |
9 | 7, 8 | fvmptg 5572 | . 2 |
10 | 4, 9 | mpdan 419 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 cvv 2730 csn 3583 cuni 3796 crn 4612 cfv 5198 c2nd 6118 |
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-sbc 2956 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-mpt 4052 df-id 4278 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-rn 4622 df-iota 5160 df-fun 5200 df-fv 5206 df-2nd 6120 |
This theorem is referenced by: 2nd0 6124 op2nd 6126 elxp6 6148 |
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