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Mirrors > Home > ILE Home > Th. List > copsex4g | Unicode version |
Description: An implicit substitution inference for 2 ordered pairs. (Contributed by NM, 5-Aug-1995.) |
Ref | Expression |
---|---|
copsex4g.1 |
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Ref | Expression |
---|---|
copsex4g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2195 |
. . . . . . 7
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2 | vex 2763 |
. . . . . . . 8
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3 | vex 2763 |
. . . . . . . 8
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4 | 2, 3 | opth 4266 |
. . . . . . 7
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5 | 1, 4 | bitri 184 |
. . . . . 6
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6 | eqcom 2195 |
. . . . . . 7
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7 | vex 2763 |
. . . . . . . 8
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8 | vex 2763 |
. . . . . . . 8
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9 | 7, 8 | opth 4266 |
. . . . . . 7
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10 | 6, 9 | bitri 184 |
. . . . . 6
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11 | 5, 10 | anbi12i 460 |
. . . . 5
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12 | 11 | anbi1i 458 |
. . . 4
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13 | 12 | a1i 9 |
. . 3
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14 | 13 | 4exbidv 1881 |
. 2
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15 | id 19 |
. . 3
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16 | copsex4g.1 |
. . 3
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17 | 15, 16 | cgsex4g 2797 |
. 2
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18 | 14, 17 | bitrd 188 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2167 ax-ext 2175 ax-sep 4147 ax-pow 4203 ax-pr 4238 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-un 3157 df-in 3159 df-ss 3166 df-pw 3603 df-sn 3624 df-pr 3625 df-op 3627 |
This theorem is referenced by: opbrop 4738 ovi3 6055 dfplpq2 7414 dfmpq2 7415 enq0breq 7496 |
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