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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1299 | 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 |
---|---|
bnj1299.1 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒)) |
Ref | Expression |
---|---|
bnj1299 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1299.1 | . 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒)) | |
2 | bnj1239 30130 | . 2 ⊢ (∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒) → ∃𝑥 ∈ 𝐴 𝜓) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∃wrex 2897 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 df-ral 2901 df-rex 2902 |
This theorem is referenced by: bnj1497 30382 bnj1498 30383 bnj1501 30389 |
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