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Mirrors > Home > MPE Home > Th. List > Mathboxes > ax-frege52c | Structured version Visualization version GIF version |
Description: One side of dfsbcq 3722. Part of Axiom 52 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax-frege52c | ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cB | . . 3 class 𝐵 | |
3 | 1, 2 | wceq 1542 | . 2 wff 𝐴 = 𝐵 |
4 | wph | . . . 4 wff 𝜑 | |
5 | vx | . . . 4 setvar 𝑥 | |
6 | 4, 5, 1 | wsbc 3720 | . . 3 wff [𝐴 / 𝑥]𝜑 |
7 | 4, 5, 2 | wsbc 3720 | . . 3 wff [𝐵 / 𝑥]𝜑 |
8 | 6, 7 | wi 4 | . 2 wff ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑) |
9 | 3, 8 | wi 4 | 1 wff (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑)) |
Colors of variables: wff setvar class |
This axiom is referenced by: frege52b 41467 frege53c 41492 frege57c 41498 |
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