Theorem 3adant3r 1237

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
3adant3r	|- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Proof of Theorem 3adant3r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 |- ( ( ph /\ ps /\ ch ) -> th )
2	1	3com13 1210	. . 3 |- ( ( ch /\ ps /\ ph ) -> th )
3	2	3adant1r 1233	. 2 |- ( ( ( ch /\ ta ) /\ ps /\ ph ) -> th )
4	3	3com13 1210	1 |- ( ( ph /\ ps /\ ( ch /\ ta ) ) -> th )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  addassnqg  7399  mulassnqg  7401  prarloc  7520  ltpopr  7612  ltexprlemfl  7626  ltexprlemfu  7628  addasssrg  7773  axaddass  7889  apmul1  8763  ltmul2  8831  lemul2  8832  dvdscmulr  11845  dvdsmulcr  11846  modremain  11952  ndvdsadd  11954  rpexp12i  12173  xblcntrps  14310  xblcntr  14311