![]() |
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 5025 | 1 ⊢ (𝐴 = 𝐵 → ∪ 𝑥 ∈ 𝐶 𝐸 = ∪ 𝑥 ∈ 𝐷 𝐸) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1542 ∪ ciun 4998 |
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-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-rex 3072 df-v 3477 df-in 3956 df-ss 3966 df-iun 5000 |
This theorem is referenced by: bnj106 33879 bnj222 33894 bnj540 33903 bnj553 33909 bnj611 33929 bnj966 33955 bnj1112 33994 |
Copyright terms: Public domain | W3C validator |