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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 324 | . . . 4 |
4 | 3 | eximi 1491 | . . 3 |
5 | 2, 4 | anim12i 321 | . 2 |
6 | df-sb 1646 | . 2 | |
7 | df-sb 1646 | . 2 | |
8 | 5, 6, 7 | 3imtr4i 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wex 1381 wsb 1645 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-sb 1646 |
This theorem is referenced by: sbbii 1648 sb6f 1684 hbsb3 1689 sbidm 1731 sbco 1842 sbcocom 1844 elsb3 1852 elsb4 1853 sbalyz 1875 hbsb4t 1889 moimv 1966 oprcl 3573 peano1 4317 peano2 4318 |
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