Mathbox for Alan Sare |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > e2bi | Structured version Visualization version GIF version |
Description: Biconditional form of e2 37877. syl6ib 240 is e2bi 37878 without virtual deductions. (Contributed by Alan Sare, 10-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e2bi.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
e2bi.2 | ⊢ (𝜒 ↔ 𝜃) |
Ref | Expression |
---|---|
e2bi | ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e2bi.1 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | e2bi.2 | . . 3 ⊢ (𝜒 ↔ 𝜃) | |
3 | 2 | biimpi 205 | . 2 ⊢ (𝜒 → 𝜃) |
4 | 1, 3 | e2 37877 | 1 ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ( wvd2 37814 |
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 196 df-an 385 df-vd2 37815 |
This theorem is referenced by: snssiALTVD 38084 eqsbc3rVD 38097 en3lplem2VD 38101 onfrALTlem3VD 38145 onfrALTlem1VD 38148 |
Copyright terms: Public domain | W3C validator |