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Mirrors > Home > MPE Home > Th. List > cbviinvg | Structured version Visualization version GIF version |
Description: Change bound variables in an indexed intersection. Usage of this theorem is discouraged because it depends on ax-13 2375. Usage of the weaker cbviinv 5046 is preferred. (Contributed by Jeff Hankins, 26-Aug-2009.) (New usage is discouraged.) |
Ref | Expression |
---|---|
cbviunvg.1 | ⊢ (𝑥 = 𝑦 → 𝐵 = 𝐶) |
Ref | Expression |
---|---|
cbviinvg | ⊢ ∩ 𝑥 ∈ 𝐴 𝐵 = ∩ 𝑦 ∈ 𝐴 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2903 | . 2 ⊢ Ⅎ𝑦𝐵 | |
2 | nfcv 2903 | . 2 ⊢ Ⅎ𝑥𝐶 | |
3 | cbviunvg.1 | . 2 ⊢ (𝑥 = 𝑦 → 𝐵 = 𝐶) | |
4 | 1, 2, 3 | cbviing 5044 | 1 ⊢ ∩ 𝑥 ∈ 𝐴 𝐵 = ∩ 𝑦 ∈ 𝐴 𝐶 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∩ ciin 4997 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-10 2139 ax-11 2155 ax-12 2175 ax-13 2375 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-ex 1777 df-nf 1781 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-nfc 2890 df-ral 3060 df-iin 4999 |
This theorem is referenced by: (None) |
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