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Mirrors > Home > MPE Home > Th. List > sbcnestgf | Structured version Visualization version Unicode version |
Description: Nest the composition of two substitutions. (Contributed by Mario Carneiro, 11-Nov-2016.) |
Ref | Expression |
---|---|
sbcnestgf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq 3281 |
. . . . 5
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2 | csbeq1 3378 |
. . . . . 6
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3 | 2 | sbceq1d 3284 |
. . . . 5
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4 | 1, 3 | bibi12d 327 |
. . . 4
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5 | 4 | imbi2d 322 |
. . 3
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6 | vex 3060 |
. . . . 5
![]() ![]() ![]() ![]() | |
7 | 6 | a1i 11 |
. . . 4
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8 | csbeq1a 3384 |
. . . . . 6
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9 | 8 | sbceq1d 3284 |
. . . . 5
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10 | 9 | adantl 472 |
. . . 4
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11 | nfnf1 1992 |
. . . . 5
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12 | 11 | nfal 2041 |
. . . 4
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13 | nfa1 1990 |
. . . . 5
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14 | nfcsb1v 3391 |
. . . . . 6
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15 | 14 | a1i 11 |
. . . . 5
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16 | sp 1948 |
. . . . 5
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17 | 13, 15, 16 | nfsbcd 3300 |
. . . 4
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18 | 7, 10, 12, 17 | sbciedf 3315 |
. . 3
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19 | 5, 18 | vtoclg 3119 |
. 2
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20 | 19 | imp 435 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-v 3059 df-sbc 3280 df-csb 3376 |
This theorem is referenced by: csbnestgf 3797 sbcnestg 3798 |
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