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Mirrors > Home > ILE Home > Th. List > sbequ12 | Unicode version |
Description: An equality theorem for substitution. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
sbequ12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbequ1 1768 |
. 2
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2 | sbequ2 1769 |
. 2
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3 | 1, 2 | impbid 129 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 |
This theorem depends on definitions: df-bi 117 df-sb 1763 |
This theorem is referenced by: sbequ12r 1772 sbequ12a 1773 sbid 1774 ax16 1813 sb8h 1854 sb8eh 1855 sb8 1856 sb8e 1857 ax16ALT 1859 sbco 1968 sbcomxyyz 1972 sb9v 1978 sb6a 1988 mopick 2104 clelab 2303 sbab 2305 nfabdw 2338 cbvralf 2696 cbvrexf 2697 cbvralsv 2719 cbvrexsv 2720 cbvrab 2735 sbhypf 2786 mob2 2917 reu2 2925 reu6 2926 sbcralt 3039 sbcrext 3040 sbcralg 3041 sbcreug 3043 cbvreucsf 3121 cbvrabcsf 3122 cbvopab1 4076 cbvopab1s 4078 csbopabg 4081 cbvmptf 4097 cbvmpt 4098 opelopabsb 4260 frind 4352 tfis 4582 findes 4602 opeliunxp 4681 ralxpf 4773 rexxpf 4774 cbviota 5183 csbiotag 5209 cbvriota 5840 csbriotag 5842 abrexex2g 6120 opabex3d 6121 opabex3 6122 abrexex2 6124 dfoprab4f 6193 finexdc 6901 ssfirab 6932 uzind4s 9588 zsupcllemstep 11940 bezoutlemmain 11993 nnwosdc 12034 cbvrald 14422 bj-bdfindes 14583 bj-findes 14615 |
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