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Mirrors > Home > ILE Home > Th. List > sbimi | Unicode version |
Description: Infer substitution into antecedent and consequent of an implication. (Contributed by NM, 25-Jun-1998.) |
Ref | Expression |
---|---|
sbimi.1 |
Ref | Expression |
---|---|
sbimi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbimi.1 | . . . 4 | |
2 | 1 | imim2i 12 | . . 3 |
3 | 1 | anim2i 339 | . . . 4 |
4 | 3 | eximi 1564 | . . 3 |
5 | 2, 4 | anim12i 336 | . 2 |
6 | df-sb 1721 | . 2 | |
7 | df-sb 1721 | . 2 | |
8 | 5, 6, 7 | 3imtr4i 200 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1453 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-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 df-sb 1721 |
This theorem is referenced by: sbbii 1723 sb6f 1759 hbsb3 1764 sbidm 1807 sbco 1919 sbcocom 1921 elsb3 1929 elsb4 1930 sbalyz 1952 hbsb4t 1966 moimv 2043 oprcl 3699 peano1 4478 peano2 4479 |
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