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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 2372. Use the weaker nfiotaw 6500 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 1807 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfiota.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfiotad 6501 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑)) |
5 | 4 | mptru 1549 | 1 ⊢ Ⅎ𝑥(℩𝑦𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1543 Ⅎwnf 1786 Ⅎwnfc 2884 ℩cio 6494 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-13 2372 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ral 3063 df-rex 3072 df-v 3477 df-in 3956 df-ss 3966 df-sn 4630 df-uni 4910 df-iota 6496 |
This theorem is referenced by: (None) |
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