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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj101 | 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 |
---|---|
bnj101.1 | ⊢ ∃𝑥𝜑 |
bnj101.2 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
bnj101 | ⊢ ∃𝑥𝜓 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj101.1 | . 2 ⊢ ∃𝑥𝜑 | |
2 | bnj101.2 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | eximii 1932 | 1 ⊢ ∃𝑥𝜓 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1875 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 |
This theorem depends on definitions: df-bi 199 df-ex 1876 |
This theorem is referenced by: bnj1023 31368 bnj1098 31371 bnj1101 31372 bnj1109 31374 bnj1468 31433 bnj907 31552 bnj1110 31567 bnj1118 31569 bnj1128 31575 bnj1145 31578 bnj1172 31586 bnj1174 31588 bnj1176 31590 |
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