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Mirrors > Home > MPE Home > Th. List > csbtt | Structured version Visualization version Unicode version |
Description: Substitution doesn't affect a constant (in which is not free). (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
csbtt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-csb 3534 | . 2 | |
2 | nfcr 2756 | . . . 4 | |
3 | sbctt 3500 | . . . 4 | |
4 | 2, 3 | sylan2 491 | . . 3 |
5 | 4 | abbi1dv 2743 | . 2 |
6 | 1, 5 | syl5eq 2668 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wnf 1708 wcel 1990 cab 2608 wnfc 2751 wsbc 3435 csb 3533 |
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-11 2034 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-nfc 2753 df-v 3202 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: csbconstgf 3545 sbnfc2 4007 constlimc 39856 |
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