Theorem bj-equsal1ti 35006

Description: Inference associated with bj-equsal1t 35005. (Contributed by BJ, 30-Sep-2018.)

Hypothesis

Ref	Expression
bj-equsal1ti.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
bj-equsal1ti	⊢ (∀𝑥(𝑥 = 𝑦 → 𝜑) ↔ 𝜑)

Proof of Theorem bj-equsal1ti

Step	Hyp	Ref	Expression
1		bj-equsal1ti.1	. 2 ⊢ Ⅎ𝑥𝜑
2		bj-equsal1t 35005	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝑥 = 𝑦 → 𝜑) ↔ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝜑) ↔ 𝜑)

Syntax hints:   → wi 4   ↔ wb 205  ∀wal 1537  Ⅎwnf 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171  ax-13 2372

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783  df-nf 1787

This theorem is referenced by:  bj-equsal1  35007  bj-equsal2  35008