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  1810  sbnf2  2035  sbcom2v  2039  sbalyz  2053  sbal1yz  2055  sbal2  2074  2eu4  2174  ralcomf  2704  gencbval  2863  unissb  3944  dfiin2g  4024  dftr5  4211  cotr  5144  cnvsym  5146  dffun2  5362  funcnveq  5419  fun11  5423