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Mirrors > Home > NFE Home > Th. List > nfcsb1 | GIF version |
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
nfcsb1.1 | ⊢ ℲxA |
Ref | Expression |
---|---|
nfcsb1 | ⊢ Ⅎx[A / x]B |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcsb1.1 | . . . 4 ⊢ ℲxA | |
2 | 1 | a1i 10 | . . 3 ⊢ ( ⊤ → ℲxA) |
3 | 2 | nfcsb1d 3166 | . 2 ⊢ ( ⊤ → Ⅎx[A / x]B) |
4 | 3 | trud 1323 | 1 ⊢ Ⅎx[A / x]B |
Colors of variables: wff setvar class |
Syntax hints: ⊤ wtru 1316 Ⅎwnfc 2476 [csb 3136 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-sbc 3047 df-csb 3137 |
This theorem is referenced by: nfcsb1v 3168 |
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