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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1265 | 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 |
---|---|
bnj1265.1 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
Ref | Expression |
---|---|
bnj1265 | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1265.1 | . . . 4 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) | |
2 | 1 | bnj1196 32510 | . . 3 ⊢ (𝜑 → ∃𝑥(𝑥 ∈ 𝐴 ∧ 𝜓)) |
3 | 2 | bnj1266 32527 | . 2 ⊢ (𝜑 → ∃𝑥𝜓) |
4 | 3 | bnj937 32487 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2111 ∃wrex 3063 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1788 df-rex 3068 |
This theorem is referenced by: bnj1253 32733 bnj1280 32736 bnj1296 32737 bnj1371 32745 bnj1497 32776 |
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