![]() |
Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
|
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 5023 | 1 ⊢ (𝐴 = 𝐵 → ∪ 𝑥 ∈ 𝐶 𝐸 = ∪ 𝑥 ∈ 𝐷 𝐸) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1539 ∪ ciun 4996 |
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 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-ext 2701 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1542 df-ex 1780 df-sb 2066 df-clab 2708 df-cleq 2722 df-clel 2808 df-rex 3069 df-v 3474 df-in 3954 df-ss 3964 df-iun 4998 |
This theorem is referenced by: bnj106 34177 bnj222 34192 bnj540 34201 bnj553 34207 bnj611 34227 bnj966 34253 bnj1112 34292 |
Copyright terms: Public domain | W3C validator |