Theorem bj-abbii 32777

Description: Remove dependency on ax-13 2246 from abbii 2739. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-abbii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
bj-abbii	⊢ {𝑥 ∣ 𝜑} = {𝑥 ∣ 𝜓}

Proof of Theorem bj-abbii

Step	Hyp	Ref	Expression
1		bj-abbi 32775	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) ↔ {𝑥 ∣ 𝜑} = {𝑥 ∣ 𝜓})
2		bj-abbii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
3	1, 2	mpgbi 1725	1 ⊢ {𝑥 ∣ 𝜑} = {𝑥 ∣ 𝜓}

Syntax hints:   ↔ wb 196   = wceq 1483  {cab 2608

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615

This theorem is referenced by:  bj-rababwv  32867