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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 6320 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓)) | |
2 | 1 | sbceq1d 3774 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒 ↔ [(℩𝑥𝜓) / 𝑦]𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 207 ∀wal 1526 [wsbc 3769 ℩cio 6305 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-rex 3141 df-sbc 3770 df-uni 4831 df-iota 6307 |
This theorem is referenced by: (None) |
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