Theorem alequcoms 1509

Description: A commutation rule for identical variable specifiers. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
alequcoms.1	⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑)

Assertion

Ref	Expression
alequcoms	⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑)

Proof of Theorem alequcoms

Step	Hyp	Ref	Expression
1		alequcom 1508	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
2		alequcoms.1	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑)
3	1, 2	syl 14	1 ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-10 1498

This theorem is referenced by:  hbae  1711  dral1  1723  drex1  1791  aev  1805  sbequi  1832