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Mirrors > Home > MPE Home > Th. List > nfxfrdOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nfxfrd 1780 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfbiiOLD.1 | ⊢ (𝜑 ↔ 𝜓) |
nfxfrdOLD.2 | ⊢ (𝜒 → Ⅎ𝑥𝜓) |
Ref | Expression |
---|---|
nfxfrdOLD | ⊢ (𝜒 → Ⅎ𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfxfrdOLD.2 | . 2 ⊢ (𝜒 → Ⅎ𝑥𝜓) | |
2 | nfbiiOLD.1 | . . 3 ⊢ (𝜑 ↔ 𝜓) | |
3 | 2 | nfbiiOLD 1836 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓) |
4 | 1, 3 | sylibr 224 | 1 ⊢ (𝜒 → Ⅎ𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 ℲwnfOLD 1709 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 |
This theorem depends on definitions: df-bi 197 df-nfOLD 1721 |
This theorem is referenced by: nfandOLD 2232 nf3andOLD 2233 nfbidOLD 2242 |
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