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Mirrors > Home > ILE Home > Th. List > csbnestgf | Unicode version |
Description: Nest the composition of two substitutions. (Contributed by NM, 23-Nov-2005.) (Proof shortened by Mario Carneiro, 10-Nov-2016.) |
Ref | Expression |
---|---|
csbnestgf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2668 |
. . 3
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2 | df-csb 2972 |
. . . . . . 7
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3 | 2 | abeq2i 2225 |
. . . . . 6
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4 | 3 | sbcbii 2936 |
. . . . 5
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5 | nfcr 2247 |
. . . . . . 7
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6 | 5 | alimi 1414 |
. . . . . 6
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7 | sbcnestgf 3017 |
. . . . . 6
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8 | 6, 7 | sylan2 282 |
. . . . 5
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9 | 4, 8 | syl5bb 191 |
. . . 4
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10 | 9 | abbidv 2232 |
. . 3
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11 | 1, 10 | sylan 279 |
. 2
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12 | df-csb 2972 |
. 2
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13 | df-csb 2972 |
. 2
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14 | 11, 12, 13 | 3eqtr4g 2172 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-sbc 2879 df-csb 2972 |
This theorem is referenced by: csbnestg 3020 csbnest1g 3021 |
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