Theorem iotasbcq 44863

Description: Theorem *14.272 in [WhiteheadRussell] p. 193. (Contributed by Andrew Salmon, 11-Jul-2011.)

Assertion

Ref	Expression
iotasbcq	⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒 ↔ [(℩𝑥𝜓) / 𝑦]𝜒))

Proof of Theorem iotasbcq

Step	Hyp	Ref	Expression
1		iotabi 6467	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (℩𝑥𝜑) = (℩𝑥𝜓))
2	1	sbceq1d 3733	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([(℩𝑥𝜑) / 𝑦]𝜒 ↔ [(℩𝑥𝜓) / 𝑦]𝜒))

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1540  [wsbc 3728  ℩cio 6452

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431  df-sbc 3729  df-ss 3906  df-uni 4851  df-iota 6454

This theorem is referenced by: (None)