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Mirrors > Home > MPE Home > Th. List > Mathboxes > e2bir | Structured version Visualization version GIF version |
Description: Right biconditional form of e2 41924. syl6ibr 255 is e2bir 41926 without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e2bir.1 | ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) |
e2bir.2 | ⊢ (𝜃 ↔ 𝜒) |
Ref | Expression |
---|---|
e2bir | ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e2bir.1 | . 2 ⊢ ( 𝜑 , 𝜓 ▶ 𝜒 ) | |
2 | e2bir.2 | . . 3 ⊢ (𝜃 ↔ 𝜒) | |
3 | 2 | biimpri 231 | . 2 ⊢ (𝜒 → 𝜃) |
4 | 1, 3 | e2 41924 | 1 ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 209 ( wvd2 41870 |
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 210 df-an 400 df-vd2 41871 |
This theorem is referenced by: trsspwALT 42111 pwtrVD 42117 eqsbc3rVD 42133 tpid3gVD 42135 onfrALTlem1VD 42183 |
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