Theorem 3simp1 594

Description: Simplification of triple conjunction.

Assertion

Ref	Expression
3simp1	|- ((ph /\ ps /\ ch) -> ph)

Proof of Theorem 3simp1

Step	Hyp	Ref	Expression
1		3simpa 591	. 2 |- ((ph /\ ps /\ ch) -> (ph /\ ps))
2	1	pm3.26d 258	1 |- ((ph /\ ps /\ ch) -> ph)

Syntax hints:   -> wi 2   /\ w3a 581

This theorem is referenced by:  limord 2283  nlimsuc 2363  find 2396  divdiv23t 4271  ltdivmult 4408  nnleltp1t 4448  suprub 4513  sqrlem20 4750  shlej1t 5356  atexch 5769  atcvatlem 5770

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

metamath.org