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Mirrors > Home > MPE Home > Th. List > cbvmptvOLD | Structured version Visualization version GIF version |
Description: Obsolete version of cbvmptv 5222 as of 17-Nov-2024. (Contributed by Mario Carneiro, 19-Feb-2013.) Add disjoint variable condition to avoid ax-13 2371. See cbvmptvg 5224 for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 17-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
cbvmptvOLD.1 | ⊢ (𝑥 = 𝑦 → 𝐵 = 𝐶) |
Ref | Expression |
---|---|
cbvmptvOLD | ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑦 ∈ 𝐴 ↦ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2904 | . 2 ⊢ Ⅎ𝑦𝐵 | |
2 | nfcv 2904 | . 2 ⊢ Ⅎ𝑥𝐶 | |
3 | cbvmptvOLD.1 | . 2 ⊢ (𝑥 = 𝑦 → 𝐵 = 𝐶) | |
4 | 1, 2, 3 | cbvmpt 5220 | 1 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑦 ∈ 𝐴 ↦ 𝐶) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1542 ↦ cmpt 5192 |
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 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-rab 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-opab 5172 df-mpt 5193 |
This theorem is referenced by: (None) |
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