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Mirrors > Home > MPE Home > Th. List > sbctt | Structured version Visualization version Unicode version |
Description: Substitution for a variable not free in a wff does not affect it. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
sbctt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq2 3438 | . . . . 5 | |
2 | 1 | bibi1d 333 | . . . 4 |
3 | 2 | imbi2d 330 | . . 3 |
4 | sbft 2379 | . . 3 | |
5 | 3, 4 | vtoclg 3266 | . 2 |
6 | 5 | imp 445 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wnf 1708 wsb 1880 wcel 1990 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-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: sbcgf 3501 csbtt 3544 mptsnunlem 33185 |
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