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Mirrors > Home > MPE Home > Th. List > Mathboxes > e3bi | Structured version Visualization version GIF version |
Description: Biconditional form of e3 42316. syl8ib 255 is e3bi 42317 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e3bi.1 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
e3bi.2 | ⊢ (𝜃 ↔ 𝜏) |
Ref | Expression |
---|---|
e3bi | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e3bi.1 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) | |
2 | e3bi.2 | . . 3 ⊢ (𝜃 ↔ 𝜏) | |
3 | 2 | biimpi 215 | . 2 ⊢ (𝜃 → 𝜏) |
4 | 1, 3 | e3 42316 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ( wvd3 42166 |
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 206 df-an 397 df-3an 1088 df-vd3 42169 |
This theorem is referenced by: en3lplem2VD 42423 |
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