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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1113 | Structured version Visualization version GIF version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1113.1 | ⊢ (𝐴 = 𝐵 → 𝐶 = 𝐷) |
Ref | Expression |
---|---|
bnj1113 | ⊢ (𝐴 = 𝐵 → ∪ 𝑥 ∈ 𝐶 𝐸 = ∪ 𝑥 ∈ 𝐷 𝐸) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1113.1 | . 2 ⊢ (𝐴 = 𝐵 → 𝐶 = 𝐷) | |
2 | 1 | iuneq1d 4735 | 1 ⊢ (𝐴 = 𝐵 → ∪ 𝑥 ∈ 𝐶 𝐸 = ∪ 𝑥 ∈ 𝐷 𝐸) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1653 ∪ ciun 4710 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 ax-5 2006 ax-6 2072 ax-7 2107 ax-9 2166 ax-10 2185 ax-11 2200 ax-12 2213 ax-ext 2777 |
This theorem depends on definitions: df-bi 199 df-an 386 df-or 875 df-tru 1657 df-ex 1876 df-nf 1880 df-sb 2065 df-clab 2786 df-cleq 2792 df-clel 2795 df-nfc 2930 df-ral 3094 df-rex 3095 df-v 3387 df-in 3776 df-ss 3783 df-iun 4712 |
This theorem is referenced by: bnj106 31455 bnj222 31470 bnj540 31479 bnj553 31485 bnj611 31505 bnj966 31531 bnj1112 31568 |
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