![]() |
Mathbox for Jonathan Ben-Naim |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj31 | 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 |
---|---|
bnj31.1 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
bnj31.2 | ⊢ (𝜓 → 𝜒) |
Ref | Expression |
---|---|
bnj31 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj31.1 | . 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) | |
2 | bnj31.2 | . . 3 ⊢ (𝜓 → 𝜒) | |
3 | 2 | reximi 3085 | . 2 ⊢ (∃𝑥 ∈ 𝐴 𝜓 → ∃𝑥 ∈ 𝐴 𝜒) |
4 | 1, 3 | syl 17 | 1 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wrex 3071 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1782 df-rex 3072 |
This theorem is referenced by: bnj168 33154 bnj110 33282 bnj906 33354 bnj1253 33441 bnj1280 33444 bnj1296 33445 bnj1371 33453 bnj1497 33484 bnj1498 33485 bnj1501 33491 |
Copyright terms: Public domain | W3C validator |