Theorem alcom 1527

Description: Theorem 19.5 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
alcom	⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑦∀𝑥𝜑)

Proof of Theorem alcom

Step	Hyp	Ref	Expression
1		ax-7 1497	. 2 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑦∀𝑥𝜑)
2		ax-7 1497	. 2 ⊢ (∀𝑦∀𝑥𝜑 → ∀𝑥∀𝑦𝜑)
3	1, 2	impbii 126	1 ⊢ (∀𝑥∀𝑦𝜑 ↔ ∀𝑦∀𝑥𝜑)

Syntax hints:   ↔ wb 105  ∀wal 1396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-7 1497

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  alrot3  1534  alrot4  1535  nfalt  1627  nfexd  1809  sbnf2  2034  sbcom2v  2038  sbalyz  2052  sbal1yz  2054  sbal2  2073  2eu4  2173  ralcomf  2695  gencbval  2853  unissb  3928  dfiin2g  4008  dftr5  4195  cotr  5125  cnvsym  5127  dffun2  5343  funcnveq  5400  fun11  5404