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Mirrors > Home > MPE Home > Th. List > sbc5 | Structured version Visualization version Unicode version |
Description: An equivalence for class substitution. (Contributed by NM, 23-Aug-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
sbc5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 3289 |
. 2
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2 | exsimpl 1740 |
. . 3
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3 | isset 3061 |
. . 3
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4 | 2, 3 | sylibr 217 |
. 2
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5 | dfsbcq2 3282 |
. . 3
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6 | eqeq2 2473 |
. . . . 5
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7 | 6 | anbi1d 716 |
. . . 4
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8 | 7 | exbidv 1779 |
. . 3
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9 | sb5 2270 |
. . 3
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10 | 5, 8, 9 | vtoclbg 3120 |
. 2
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11 | 1, 4, 10 | pm5.21nii 359 |
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-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-v 3059 df-sbc 3280 |
This theorem is referenced by: sbc6g 3305 sbc7 3307 sbciegft 3310 sbccomlem 3350 csb2 3377 rexsns 4016 rexsnsOLD 4017 iunxsngf 28227 sbccom2lem 32410 pm13.192 36806 pm13.195 36809 2sbc5g 36812 iotasbc 36815 pm14.122b 36819 iotasbc5 36827 |
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