Theorem bj-equsal1ti 37777

Description: Inference associated with bj-equsal1t 37776. (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 37776	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝑥 = 𝑦 → 𝜑) ↔ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝜑) ↔ 𝜑)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209  ∀wal 1567  Ⅎwnf 1815

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212  ax-13 2401

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-nf 1816

This theorem is used by:  bj-equsal1  37778  bj-equsal2  37779