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Mirrors > Home > ILE Home > Th. List > simplbi2comg | GIF version |
Description: Implication form of simplbi2com 1333. (Contributed by Alan Sare, 22-Jul-2012.) |
Ref | Expression |
---|---|
simplbi2comg | ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → (𝜒 → (𝜓 → 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi2 121 | . 2 ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → ((𝜓 ∧ 𝜒) → 𝜑)) | |
2 | 1 | expcomd 1330 | 1 ⊢ ((𝜑 ↔ (𝜓 ∧ 𝜒)) → (𝜒 → (𝜓 → 𝜑))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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