Theorem aecoms-o 36559

Description: A commutation rule for identical variable specifiers. Version of aecoms 2428 using ax-c11 36544. (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 36558	. 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 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-c5 36540  ax-c4 36541  ax-c7 36542  ax-c10 36543  ax-c11 36544  ax-c9 36547

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787

This theorem is referenced by:  hbae-o  36560  dral1-o  36561  dvelimf-o  36586  aev-o  36588  ax12indalem  36602  ax12inda2ALT  36603