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Mirrors > Home > MPE Home > Th. List > 4sqlem2 | Structured version Visualization version Unicode version |
Description: Lemma for 4sq 15668. Change bound variables in . (Contributed by Mario Carneiro, 14-Jul-2014.) |
Ref | Expression |
---|---|
4sq.1 |
Ref | Expression |
---|---|
4sqlem2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4sq.1 | . . 3 | |
2 | 1 | eleq2i 2693 | . 2 |
3 | id 22 | . . . . . . 7 | |
4 | ovex 6678 | . . . . . . 7 | |
5 | 3, 4 | syl6eqel 2709 | . . . . . 6 |
6 | 5 | a1i 11 | . . . . 5 |
7 | 6 | rexlimdvva 3038 | . . . 4 |
8 | 7 | rexlimivv 3036 | . . 3 |
9 | oveq1 6657 | . . . . . . . . 9 | |
10 | 9 | oveq1d 6665 | . . . . . . . 8 |
11 | 10 | oveq1d 6665 | . . . . . . 7 |
12 | 11 | eqeq2d 2632 | . . . . . 6 |
13 | 12 | 2rexbidv 3057 | . . . . 5 |
14 | oveq1 6657 | . . . . . . . . 9 | |
15 | 14 | oveq2d 6666 | . . . . . . . 8 |
16 | 15 | oveq1d 6665 | . . . . . . 7 |
17 | 16 | eqeq2d 2632 | . . . . . 6 |
18 | 17 | 2rexbidv 3057 | . . . . 5 |
19 | 13, 18 | cbvrex2v 3180 | . . . 4 |
20 | oveq1 6657 | . . . . . . . . . 10 | |
21 | 20 | oveq1d 6665 | . . . . . . . . 9 |
22 | 21 | oveq2d 6666 | . . . . . . . 8 |
23 | 22 | eqeq2d 2632 | . . . . . . 7 |
24 | oveq1 6657 | . . . . . . . . . 10 | |
25 | 24 | oveq2d 6666 | . . . . . . . . 9 |
26 | 25 | oveq2d 6666 | . . . . . . . 8 |
27 | 26 | eqeq2d 2632 | . . . . . . 7 |
28 | 23, 27 | cbvrex2v 3180 | . . . . . 6 |
29 | eqeq1 2626 | . . . . . . 7 | |
30 | 29 | 2rexbidv 3057 | . . . . . 6 |
31 | 28, 30 | syl5bb 272 | . . . . 5 |
32 | 31 | 2rexbidv 3057 | . . . 4 |
33 | 19, 32 | syl5bb 272 | . . 3 |
34 | 8, 33 | elab3 3358 | . 2 |
35 | 2, 34 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 cab 2608 wrex 2913 cvv 3200 (class class class)co 6650 caddc 9939 c2 11070 cz 11377 cexp 12860 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 |
This theorem is referenced by: 4sqlem3 15654 4sqlem4 15656 4sqlem18 15666 4sq 15668 |
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