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Mirrors > Home > MPE Home > Th. List > sbequ12r | Structured version Visualization version Unicode version |
Description: An equality theorem for substitution. (Contributed by NM, 6-Oct-2004.) (Proof shortened by Andrew Salmon, 21-Jun-2011.) |
Ref | Expression |
---|---|
sbequ12r |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbequ12 2111 | . . 3 | |
2 | 1 | bicomd 213 | . 2 |
3 | 2 | equcoms 1947 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 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 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 df-sb 1881 |
This theorem is referenced by: sbequ12a 2113 sbid 2114 sb5rf 2422 sb6rf 2423 2sb5rf 2451 2sb6rf 2452 opeliunxp 5170 isarep1 5977 findes 7096 axrepndlem1 9414 axrepndlem2 9415 nn0min 29567 esumcvg 30148 bj-abbi 32775 bj-sbidmOLD 32831 wl-nfs1t 33324 wl-sb6rft 33330 wl-equsb4 33338 wl-ax11-lem5 33366 sbcalf 33917 sbcexf 33918 opeliun2xp 42111 |
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