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| Mirrors > Home > MPE Home > Th. List > nfsbc1 | Structured version Visualization version GIF version | ||
| Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) |
| Ref | Expression |
|---|---|
| nfsbc1.1 | ⊢ Ⅎ𝑥𝐴 |
| Ref | Expression |
|---|---|
| nfsbc1 | ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfsbc1.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
| 2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
| 3 | 2 | nfsbc1d 3806 | . 2 ⊢ (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑) |
| 4 | 3 | mptru 1547 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
| Colors of variables: wff setvar class |
| Syntax hints: ⊤wtru 1541 Ⅎwnf 1783 Ⅎwnfc 2890 [wsbc 3788 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-nf 1784 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-sbc 3789 |
| This theorem is referenced by: nfsbc1v 3808 riotass2 7418 riotass 7419 uzwo4 45058 |
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