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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj534 | 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 |
---|---|
bnj534.1 | ⊢ (𝜒 → (∃𝑥𝜑 ∧ 𝜓)) |
Ref | Expression |
---|---|
bnj534 | ⊢ (𝜒 → ∃𝑥(𝜑 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj534.1 | . 2 ⊢ (𝜒 → (∃𝑥𝜑 ∧ 𝜓)) | |
2 | 19.41v 1914 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ (∃𝑥𝜑 ∧ 𝜓)) | |
3 | 1, 2 | sylibr 224 | 1 ⊢ (𝜒 → ∃𝑥(𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 ∃wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: bnj600 30989 bnj852 30991 |
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