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Mirrors > Home > MPE Home > Th. List > sbcnestg | Structured version Visualization version Unicode version |
Description: Nest the composition of two substitutions. (Contributed by NM, 27-Nov-2005.) (Proof shortened by Mario Carneiro, 11-Nov-2016.) |
Ref | Expression |
---|---|
sbcnestg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . . 3 | |
2 | 1 | ax-gen 1722 | . 2 |
3 | sbcnestgf 3995 | . 2 | |
4 | 2, 3 | mpan2 707 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wnf 1708 wcel 1990 wsbc 3435 csb 3533 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: sbcco3g 3999 |
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