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Mirrors > Home > NFE Home > Th. List > sbsbc | Unicode version |
Description: Show that df-sb 1649 and df-sbc 3047 are equivalent when the class term in df-sbc 3047 is a setvar variable. This theorem lets us reuse theorems based on df-sb 1649 for proofs involving df-sbc 3047. (Contributed by NM, 31-Dec-2016.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
sbsbc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2353 | . 2 | |
2 | dfsbcq2 3049 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wsb 1648 wsbc 3046 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-clab 2340 df-cleq 2346 df-clel 2349 df-sbc 3047 |
This theorem is referenced by: spsbc 3058 sbcid 3062 sbcco 3068 sbcco2 3069 sbcie2g 3079 eqsbc3 3085 sbcralt 3118 csbid 3143 sbnfc2 3196 csbabg 3197 cbvralcsf 3198 cbvreucsf 3200 cbvrabcsf 3201 |
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