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Mirrors > Home > MPE Home > Th. List > Mathboxes > e2bir | Structured version Visualization version GIF version |
Description: Right biconditional form of e2 40971. syl6ibr 254 is e2bir 40973 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 230 | . 2 ⊢ (𝜒 → 𝜃) |
4 | 1, 3 | e2 40971 | 1 ⊢ ( 𝜑 , 𝜓 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ( wvd2 40917 |
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-vd2 40918 |
This theorem is referenced by: trsspwALT 41158 pwtrVD 41164 eqsbc3rVD 41180 tpid3gVD 41182 onfrALTlem1VD 41230 |
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