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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-sblimt | Structured version Visualization version Unicode version |
Description: Substitution with a variable not free in antecedent affects only the consequent. Closed form of sbrim 2225. (Contributed by Wolf Lammen, 26-Jul-2019.) |
Ref | Expression |
---|---|
wl-sblimt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbim 2224 |
. 2
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2 | sbft 2208 |
. . 3
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3 | 2 | imbi2d 318 |
. 2
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4 | 1, 3 | syl5bb 261 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-ex 1664 df-nf 1668 df-sb 1798 |
This theorem is referenced by: (None) |
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