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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege66b | Structured version Visualization version GIF version |
Description: Swap antecedents of frege65b 39043. Proposition 66 of [Frege1879] p. 54. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege66b | ⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥(𝜒 → 𝜑) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege65b 39043 | . 2 ⊢ (∀𝑥(𝜒 → 𝜑) → (∀𝑥(𝜑 → 𝜓) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓))) | |
2 | ax-frege8 38942 | . 2 ⊢ ((∀𝑥(𝜒 → 𝜑) → (∀𝑥(𝜑 → 𝜓) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓))) → (∀𝑥(𝜑 → 𝜓) → (∀𝑥(𝜒 → 𝜑) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓)))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥(𝜒 → 𝜑) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1654 [wsb 2067 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-10 2192 ax-12 2220 ax-13 2389 ax-frege1 38923 ax-frege2 38924 ax-frege8 38942 ax-frege58b 39034 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-ex 1879 df-nf 1883 df-sb 2068 |
This theorem is referenced by: (None) |
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