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Mirrors > Home > MPE Home > Th. List > sbc19.21g | Structured version Visualization version Unicode version |
Description: Substitution for a variable not free in antecedent affects only the consequent. (Contributed by NM, 11-Oct-2004.) |
Ref | Expression |
---|---|
sbcgf.1 |
Ref | Expression |
---|---|
sbc19.21g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcimg 3477 | . 2 | |
2 | sbcgf.1 | . . . 4 | |
3 | 2 | sbcgf 3501 | . . 3 |
4 | 3 | imbi1d 331 | . 2 |
5 | 1, 4 | bitrd 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wnf 1708 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-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: bnj121 30940 bnj124 30941 bnj130 30944 bnj207 30951 bnj611 30988 bnj1000 31011 |
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