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Mirrors > Home > MPE Home > Th. List > sbim | Structured version Visualization version Unicode version |
Description: Implication inside and outside of substitution are equivalent. (Contributed by NM, 14-May-1993.) |
Ref | Expression |
---|---|
sbim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbi1 2232 |
. 2
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2 | sbi2 2233 |
. 2
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3 | 1, 2 | impbii 192 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-12 1944 ax-13 2102 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-ex 1675 df-nf 1679 df-sb 1809 |
This theorem is referenced by: sbrim 2236 sblim 2237 sbor 2238 sban 2239 sbbi 2241 sbequ8ALT 2247 sbcimg 3321 mo5f 28176 iuninc 28230 suppss2fOLD 28290 suppss2f 28291 esumpfinvalf 28948 bj-sbnf 31487 wl-sbrimt 31924 wl-sblimt 31925 frege58bcor 36545 frege60b 36547 frege65b 36552 ellimcabssub0 37783 |
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