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Mirrors > Home > NFE Home > Th. List > syl6eleqr | Unicode version |
Description: A membership and equality inference. (Contributed by NM, 24-Apr-2005.) |
Ref | Expression |
---|---|
syl6eleqr.1 | |
syl6eleqr.2 |
Ref | Expression |
---|---|
syl6eleqr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6eleqr.1 | . 2 | |
2 | syl6eleqr.2 | . . 3 | |
3 | 2 | eqcomi 2357 | . 2 |
4 | 1, 3 | syl6eleq 2443 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 wcel 1710 |
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-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-cleq 2346 df-clel 2349 |
This theorem is referenced by: reiotacl2 4363 nnadjoinpw 4521 sfinltfin 4535 vinf 4555 nulnnn 4556 ecopqsi 5981 ncidg 6122 |
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