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Mirrors > Home > MPE Home > Th. List > nf3andOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nf3and 1815 as of 6-Oct-2021. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfandOLD.1 | ⊢ (𝜑 → Ⅎ𝑥𝜓) |
nfandOLD.2 | ⊢ (𝜑 → Ⅎ𝑥𝜒) |
nfand.3OLD | ⊢ (𝜑 → Ⅎ𝑥𝜃) |
Ref | Expression |
---|---|
nf3andOLD | ⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒 ∧ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 1033 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) ↔ ((𝜓 ∧ 𝜒) ∧ 𝜃)) | |
2 | nfandOLD.1 | . . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜓) | |
3 | nfandOLD.2 | . . . 4 ⊢ (𝜑 → Ⅎ𝑥𝜒) | |
4 | 2, 3 | nfandOLD 2220 | . . 3 ⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒)) |
5 | nfand.3OLD | . . 3 ⊢ (𝜑 → Ⅎ𝑥𝜃) | |
6 | 4, 5 | nfandOLD 2220 | . 2 ⊢ (𝜑 → Ⅎ𝑥((𝜓 ∧ 𝜒) ∧ 𝜃)) |
7 | 1, 6 | nfxfrdOLD 1826 | 1 ⊢ (𝜑 → Ⅎ𝑥(𝜓 ∧ 𝜒 ∧ 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 ℲwnfOLD 1700 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-ex 1696 df-nf 1701 df-nfOLD 1712 |
This theorem is referenced by: (None) |
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