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Mirrors > Home > ILE Home > Th. List > sbcco2 | Unicode version |
Description: A composition law for class substitution. Importantly, may occur free in the class expression substituted for . (Contributed by NM, 5-Sep-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
sbcco2.1 |
Ref | Expression |
---|---|
sbcco2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbsbc 2951 | . 2 | |
2 | nfv 1515 | . . 3 | |
3 | sbcco2.1 | . . . . 5 | |
4 | 3 | equcoms 1695 | . . . 4 |
5 | dfsbcq 2949 | . . . . 5 | |
6 | 5 | bicomd 140 | . . . 4 |
7 | 4, 6 | syl 14 | . . 3 |
8 | 2, 7 | sbie 1778 | . 2 |
9 | 1, 8 | bitr3i 185 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1342 wsb 1749 wsbc 2947 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-sbc 2948 |
This theorem is referenced by: (None) |
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