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Mirrors > Home > MPE Home > Th. List > Mathboxes > iotasbcq | Structured version Visualization version GIF version |
Description: Theorem *14.272 in [WhiteheadRussell] p. 193. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotasbcq | ⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒 ↔ [(℩𝑥𝜓) / 𝑦]𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotabi 6163 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓)) | |
2 | 1 | sbceq1d 3688 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒 ↔ [(℩𝑥𝜓) / 𝑦]𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 198 ∀wal 1505 [wsbc 3683 ℩cio 6152 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-ext 2750 |
This theorem depends on definitions: df-bi 199 df-an 388 df-ex 1743 df-sb 2016 df-clab 2759 df-cleq 2771 df-clel 2846 df-rex 3094 df-sbc 3684 df-uni 4714 df-iota 6154 |
This theorem is referenced by: (None) |
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