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Mirrors > Home > MPE Home > Th. List > nfralwOLD | Structured version Visualization version GIF version |
Description: Obsolete version of nfralw 3307 as of 13-Dec-2024. (Contributed by NM, 1-Sep-1999.) (Revised by Gino Giotto, 10-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfralw.1 | ⊢ Ⅎ𝑥𝐴 |
nfralw.2 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfralwOLD | ⊢ Ⅎ𝑥∀𝑦 ∈ 𝐴 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1805 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfralw.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
4 | nfralw.2 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
5 | 4 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
6 | 1, 3, 5 | nfraldw 3305 | . 2 ⊢ (⊤ → Ⅎ𝑥∀𝑦 ∈ 𝐴 𝜑) |
7 | 6 | mptru 1547 | 1 ⊢ Ⅎ𝑥∀𝑦 ∈ 𝐴 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1541 Ⅎwnf 1784 Ⅎwnfc 2882 ∀wral 3060 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-10 2136 ax-11 2153 ax-12 2170 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1543 df-ex 1781 df-nf 1785 df-clel 2809 df-nfc 2884 df-ral 3061 |
This theorem is referenced by: (None) |
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