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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 2994 | . 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 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: bnj168 30052 bnj110 30182 bnj906 30254 bnj1253 30339 bnj1280 30342 bnj1296 30343 bnj1371 30351 bnj1497 30382 bnj1498 30383 bnj1501 30389 |
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