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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege58acor | Structured version Visualization version GIF version |
Description: Lemma for frege59a 37191. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege58acor | ⊢ (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege58a 37189 | . 2 ⊢ (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → if-(𝜑, (𝜓 → 𝜒), (𝜃 → 𝜏))) | |
2 | ifpimim 36873 | . 2 ⊢ (if-(𝜑, (𝜓 → 𝜒), (𝜃 → 𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏))) | |
3 | 1, 2 | syl 17 | 1 ⊢ (((𝜓 → 𝜒) ∧ (𝜃 → 𝜏)) → (if-(𝜑, 𝜓, 𝜃) → if-(𝜑, 𝜒, 𝜏))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 if-wif 1006 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-frege58a 37189 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-ifp 1007 |
This theorem is referenced by: frege59a 37191 frege60a 37192 frege62a 37194 |
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