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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1239 | 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 |
---|---|
bnj1239 | ⊢ (∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒) → ∃𝑥 ∈ 𝐴 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 472 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜓) | |
2 | 1 | reximi 2994 | 1 ⊢ (∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒) → ∃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: bnj1238 30131 bnj1299 30143 bnj66 30184 |
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