Theorem bj-equsal1ti 36738

Description: Inference associated with bj-equsal1t 36737. (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 36737	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝑥 = 𝑦 → 𝜑) ↔ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝜑) ↔ 𝜑)

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1535  Ⅎwnf 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-12 2173  ax-13 2374

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778  df-nf 1782

This theorem is referenced by:  bj-equsal1  36739  bj-equsal2  36740