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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 6500 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓)) | |
2 | 1 | sbceq1d 3775 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒 ↔ [(℩𝑥𝜓) / 𝑦]𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∀wal 1531 [wsbc 3770 ℩cio 6484 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-v 3468 df-sbc 3771 df-in 3948 df-ss 3958 df-uni 4901 df-iota 6486 |
This theorem is referenced by: (None) |
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