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Mirrors > Home > MPE Home > Th. List > nfceqiOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of nfceqi 2972 as of 19-Jun-2023. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfcxfr.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
nfceqiOLD | ⊢ (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1804 | . . 3 ⊢ Ⅎ𝑥⊤ | |
2 | nfcxfr.1 | . . . 4 ⊢ 𝐴 = 𝐵 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → 𝐴 = 𝐵) |
4 | 1, 3 | nfceqdf 2971 | . 2 ⊢ (⊤ → (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵)) |
5 | 4 | mptru 1543 | 1 ⊢ (Ⅎ𝑥𝐴 ↔ Ⅎ𝑥𝐵) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 = wceq 1536 ⊤wtru 1537 Ⅎwnfc 2960 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-12 2176 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-tru 1539 df-ex 1780 df-nf 1784 df-cleq 2813 df-clel 2892 df-nfc 2962 |
This theorem is referenced by: (None) |
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