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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1198 | 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 |
---|---|
bnj1198.1 | ⊢ (𝜑 → ∃𝑥𝜓) |
bnj1198.2 | ⊢ (𝜓′ ↔ 𝜓) |
Ref | Expression |
---|---|
bnj1198 | ⊢ (𝜑 → ∃𝑥𝜓′) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1198.1 | . 2 ⊢ (𝜑 → ∃𝑥𝜓) | |
2 | bnj1198.2 | . . 3 ⊢ (𝜓′ ↔ 𝜓) | |
3 | 2 | exbii 1845 | . 2 ⊢ (∃𝑥𝜓′ ↔ ∃𝑥𝜓) |
4 | 1, 3 | sylibr 234 | 1 ⊢ (𝜑 → ∃𝑥𝜓′) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 206 ∃wex 1776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 |
This theorem depends on definitions: df-bi 207 df-ex 1777 |
This theorem is referenced by: bnj1209 34789 bnj1275 34806 bnj1340 34816 bnj1345 34817 bnj605 34900 bnj607 34909 bnj906 34923 bnj908 34924 bnj1189 35002 bnj1450 35043 bnj1312 35051 |
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