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Mirrors > Home > MPE Home > Th. List > itg1addlem3 | Structured version Visualization version Unicode version |
Description: Lemma for itg1add 22659. (Contributed by Mario Carneiro, 26-Jun-2014.) |
Ref | Expression |
---|---|
i1fadd.1 |
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i1fadd.2 |
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itg1add.3 |
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Ref | Expression |
---|---|
itg1addlem3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2455 |
. . . . 5
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2 | eqeq1 2455 |
. . . . 5
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3 | 1, 2 | bi2anan9 884 |
. . . 4
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4 | sneq 3978 |
. . . . . . 7
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5 | 4 | imaeq2d 5168 |
. . . . . 6
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6 | sneq 3978 |
. . . . . . 7
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7 | 6 | imaeq2d 5168 |
. . . . . 6
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8 | 5, 7 | ineqan12d 3636 |
. . . . 5
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9 | 8 | fveq2d 5869 |
. . . 4
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10 | 3, 9 | ifbieq2d 3906 |
. . 3
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11 | itg1add.3 |
. . 3
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12 | c0ex 9637 |
. . . 4
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13 | fvex 5875 |
. . . 4
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14 | 12, 13 | ifex 3949 |
. . 3
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15 | 10, 11, 14 | ovmpt2a 6427 |
. 2
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16 | iffalse 3890 |
. 2
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17 | 15, 16 | sylan9eq 2505 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 ax-1cn 9597 ax-icn 9598 ax-addcl 9599 ax-mulcl 9601 ax-i2m1 9607 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fv 5590 df-ov 6293 df-oprab 6294 df-mpt2 6295 |
This theorem is referenced by: itg1addlem4 22657 itg1addlem5 22658 |
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