Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1254 | 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 |
---|---|
bnj1254.1 | ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏)) |
Ref | Expression |
---|---|
bnj1254 | ⊢ (𝜑 → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1254.1 | . 2 ⊢ (𝜑 ↔ (𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏)) | |
2 | id 22 | . . 3 ⊢ (𝜏 → 𝜏) | |
3 | 2 | bnj708 32020 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃 ∧ 𝜏) → 𝜏) |
4 | 1, 3 | sylbi 219 | 1 ⊢ (𝜑 → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 ∧ w-bnj17 31949 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 209 df-an 399 df-bnj17 31950 |
This theorem is referenced by: bnj554 32164 bnj557 32166 bnj967 32210 bnj999 32223 bnj907 32232 bnj1118 32249 bnj1128 32255 bnj1253 32282 bnj1450 32315 |
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