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Mirrors > Home > ILE Home > Th. List > sblim | Unicode version |
Description: Substitution with a variable not free in consequent affects only the antecedent. (Contributed by NM, 14-Nov-2013.) (Revised by Mario Carneiro, 4-Oct-2016.) |
Ref | Expression |
---|---|
sblim.1 |
Ref | Expression |
---|---|
sblim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbim 1904 | . 2 | |
2 | sblim.1 | . . . 4 | |
3 | 2 | sbf 1735 | . . 3 |
4 | 3 | imbi2i 225 | . 2 |
5 | 1, 4 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wnf 1421 wsb 1720 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 |
This theorem is referenced by: sbnf2 1934 sbmo 2036 |
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