Theorem aecoms-o 35050

Description: A commutation rule for identical variable specifiers. Version of aecoms 2393 using ax-c11 35035. (Contributed by NM, 10-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

Ref	Expression
aecoms-o	⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑)

Proof of Theorem aecoms-o

Step	Hyp	Ref	Expression
1		aecom-o 35049	. 2 ⊢ (∀𝑦 𝑦 = 𝑥 → ∀𝑥 𝑥 = 𝑦)
2		alequcoms-o.1	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑)
3	1, 2	syl 17	1 ⊢ (∀𝑦 𝑦 = 𝑥 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1599

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-c5 35031  ax-c4 35032  ax-c7 35033  ax-c10 35034  ax-c11 35035  ax-c9 35038

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824

This theorem is referenced by:  hbae-o  35051  dral1-o  35052  dvelimf-o  35077  aev-o  35079  ax12indalem  35093  ax12inda2ALT  35094