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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 3738 | . 2 ⊢ (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑) |
4 | 3 | mptru 1545 | 1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1539 Ⅎwnf 1785 Ⅎwnfc 2936 [wsbc 3720 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-sbc 3721 |
This theorem is referenced by: nfsbc1v 3740 riotass2 7123 riotass 7124 uzwo4 41687 |
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