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Mirrors > Home > MPE Home > Th. List > sbcom4 | Structured version Visualization version Unicode version |
Description: Commutativity law for substitution. This theorem was incorrectly used as our previous version of pm11.07 2447 but may still be useful. (Contributed by Andrew Salmon, 17-Jun-2011.) (Proof shortened by Jim Kingdon, 22-Jan-2018.) |
Ref | Expression |
---|---|
sbcom4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . . 3 | |
2 | 1 | sbf 2380 | . 2 |
3 | nfv 1843 | . . . 4 | |
4 | 3 | sbf 2380 | . . 3 |
5 | 4 | sbbii 1887 | . 2 |
6 | 3 | sbf 2380 | . . . 4 |
7 | 6 | sbbii 1887 | . . 3 |
8 | 1 | sbf 2380 | . . 3 |
9 | 7, 8 | bitri 264 | . 2 |
10 | 2, 5, 9 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wsb 1880 |
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-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-nf 1710 df-sb 1881 |
This theorem is referenced by: (None) |
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