Theorem albid 1772

Description: Formula-building rule for universal quantifier (deduction rule). (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
albid.1	|- F/xph
albid.2	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
albid	|- (ph -> (A.xps <-> A.xch))

Proof of Theorem albid

Step	Hyp	Ref	Expression
1		albid.1	. . 3 |- F/xph
2	1	nfri 1762	. 2 |- (ph -> A.xph)
3		albid.2	. 2 |- (ph -> (ps <-> ch))
4	2, 3	albidh 1590	1 |- (ph -> (A.xps <-> A.xch))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  nfbidf  1774  ax11v2  1992  sbcom  2089  sbal2  2134  ax11eq  2193  ax11el  2194  ax11v2-o  2201  eubid  2211  ralbida  2628  raleqf  2803  intab  3956