Theorem iotabii 4362

Description: Formula-building deduction rule for iota. (Contributed by Mario Carneiro, 2-Oct-2015.)

Hypothesis

Ref	Expression
iotabii.1	⊢ (φ ↔ ψ)

Assertion

Ref	Expression
iotabii	⊢ (℩xφ) = (℩xψ)

Proof of Theorem iotabii

Step	Hyp	Ref	Expression
1		iotabi 4349	. 2 ⊢ (∀x(φ ↔ ψ) → (℩xφ) = (℩xψ))
2		iotabii.1	. 2 ⊢ (φ ↔ ψ)
3	1, 2	mpg 1548	1 ⊢ (℩xφ) = (℩xψ)

Syntax hints:   ↔ wb 176   = wceq 1642  ℩cio 4338

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-rex 2621  df-uni 3893  df-iota 4340

This theorem is referenced by: (None)