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Mirrors > Home > NFE Home > Th. List > prid1g | Unicode version |
Description: An unordered pair contains its first member. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by Stefan Allan, 8-Nov-2008.) |
Ref | Expression |
---|---|
prid1g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2353 | . . 3 | |
2 | 1 | orci 379 | . 2 |
3 | elprg 3750 | . 2 | |
4 | 2, 3 | mpbiri 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wo 357 wceq 1642 wcel 1710 cpr 3738 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 |
This theorem is referenced by: prid2g 3826 prid1 3827 opkth1g 4130 |
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