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Mirrors > Home > MPE Home > Th. List > nfiota | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for the ℩ class. Usage of this theorem is discouraged because it depends on ax-13 2380. Use the weaker nfiotaw 6529 when possible. (Contributed by NM, 23-Aug-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfiota.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfiota | ⊢ Ⅎ𝑥(℩𝑦𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1802 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfiota.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfiotad 6530 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑)) |
5 | 4 | mptru 1544 | 1 ⊢ Ⅎ𝑥(℩𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1538 Ⅎwnf 1781 Ⅎwnfc 2893 ℩cio 6523 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1793 ax-4 1807 ax-5 1909 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2158 ax-12 2178 ax-13 2380 ax-ext 2711 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-tru 1540 df-ex 1778 df-nf 1782 df-sb 2065 df-clab 2718 df-cleq 2732 df-clel 2819 df-nfc 2895 df-ral 3068 df-rex 3077 df-v 3490 df-ss 3993 df-sn 4649 df-uni 4932 df-iota 6525 |
This theorem is referenced by: (None) |
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