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Mirrors > Home > MPE Home > Th. List > nfcrALT | Structured version Visualization version GIF version |
Description: Alternate version of nfcr 2902. Avoids ax-8 2114 but uses ax-12 2176. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
nfcrALT | ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥 𝑦 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nfc 2899 | . 2 ⊢ (Ⅎ𝑥𝐴 ↔ ∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴) | |
2 | sp 2181 | . 2 ⊢ (∀𝑦Ⅎ𝑥 𝑦 ∈ 𝐴 → Ⅎ𝑥 𝑦 ∈ 𝐴) | |
3 | 1, 2 | sylbi 220 | 1 ⊢ (Ⅎ𝑥𝐴 → Ⅎ𝑥 𝑦 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1537 Ⅎwnf 1786 ∈ wcel 2112 Ⅎwnfc 2897 |
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 1912 ax-6 1971 ax-7 2016 ax-12 2176 |
This theorem depends on definitions: df-bi 210 df-ex 1783 df-nfc 2899 |
This theorem is referenced by: (None) |
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