Theorem bnj524 34752

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj524.1	⊢ (𝜑 ↔ 𝜓)
bnj524.2	⊢ 𝐴 ∈ V

Assertion

Ref	Expression
bnj524	⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓)

Proof of Theorem bnj524

Step	Hyp	Ref	Expression
1		bnj524.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2	1	sbcbii 3845	1 ⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓)

Syntax hints:   ↔ wb 206   ∈ wcel 2107  Vcvv 3479  [wsbc 3787

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-sbc 3788

This theorem is referenced by: (None)