Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > e3bir | Structured version Visualization version GIF version |
Description: Right biconditional form of e3 38964. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e3bir.1 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
e3bir.2 | ⊢ (𝜏 ↔ 𝜃) |
Ref | Expression |
---|---|
e3bir | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e3bir.1 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) | |
2 | e3bir.2 | . . 3 ⊢ (𝜏 ↔ 𝜃) | |
3 | 2 | biimpri 218 | . 2 ⊢ (𝜃 → 𝜏) |
4 | 1, 3 | e3 38964 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ( wvd3 38803 |
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 197 df-an 386 df-3an 1039 df-vd3 38806 |
This theorem is referenced by: en3lplem2VD 39079 |
Copyright terms: Public domain | W3C validator |