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Mirrors > Home > MPE Home > Th. List > sbcim1 | Structured version Visualization version Unicode version |
Description: Distribution of class substitution over implication. One direction of sbcimg 3477 that holds for proper classes. (Contributed by NM, 17-Aug-2018.) |
Ref | Expression |
---|---|
sbcim1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 3445 | . 2 | |
2 | sbcimg 3477 | . . 3 | |
3 | 2 | biimpd 219 | . 2 |
4 | 1, 3 | mpcom 38 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cvv 3200 wsbc 3435 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 df-sbc 3436 |
This theorem is referenced by: sbcimdv 3498 sbcimdvOLD 3499 frege59c 38216 frege60c 38217 frege62c 38219 frege65c 38222 frege70 38227 frege72 38229 frege92 38249 frege120 38277 |
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