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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege58bcor | Structured version Visualization version GIF version |
Description: Lemma for frege59b 40241. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege58bcor | ⊢ (∀𝑥(𝜑 → 𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege58b 40238 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → [𝑦 / 𝑥](𝜑 → 𝜓)) | |
2 | sbim 2305 | . 2 ⊢ ([𝑦 / 𝑥](𝜑 → 𝜓) ↔ ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓)) | |
3 | 1, 2 | sylib 220 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) → ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1529 [wsb 2063 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-10 2139 ax-12 2170 ax-frege58b 40238 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-ex 1775 df-nf 1779 df-sb 2064 |
This theorem is referenced by: frege59b 40241 frege62b 40244 |
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