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 1764 | . 2 ⊢ (∃𝑥𝜓′ ↔ ∃𝑥𝜓) |
4 | 1, 3 | sylibr 223 | 1 ⊢ (𝜑 → ∃𝑥𝜓′) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 ∃wex 1695 |
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-ex 1696 |
This theorem is referenced by: bnj1209 30121 bnj1275 30138 bnj1340 30148 bnj1345 30149 bnj605 30231 bnj607 30240 bnj906 30254 bnj908 30255 bnj1189 30331 bnj1450 30372 bnj1312 30380 |
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